Free NEET Physics multiple-choice questions on Dimensional Analysis. Attempt each question and reveal the answer with a full explanation.
The dimensions [ML 2T -2 ] belong to: Energy Force Momentum Power The dimensions of 'Bulk Modulus' are same as those of: Stress Strain Force Work The dimensions of Planck's constant are the same as those of: Angular momentum Linear momentum Work Power If force ( F ), acceleration ( A ) and time ( T ) are chosen as the fundamental physical quantities, find the dimensions of energy. [FAT 2] [FAT] [FA 2T] [FA 2T 2] The dimensions of Universal Gravitational Constant are: [M -1 L 3T -2 ] [ML 2T -1 ] [M -2 L 3T -2 ] [M -1 L 2T -1 ] Which of the following pairs of physical quantities has the same dimensions? Work and Torque Force and Impulse Angular momentum and Linear momentum Pressure and Surface tension The dimensions of solar constant (energy falling on unit area per unit time) are: [MT -3 ] [ML 2T -2 ] [MLT -2 ] [MT -2 ] The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by f = cm x k y , where c is a dimensionless constant. The values of x and y are: x = -1/2, y = 1/2 x = 1/2, y = -1/2 x = 1/2, y = 1/2 x = -1/2, y = -1/2 The dimension of Coefficient of Viscosity is: [ML -1 T -1 ] [ML -1 T -2 ] [ML 2T -1 ] [MLT -1 ] If the dimensions of a physical quantity are given by M a L b T c , then the physical quantity will be: Pressure if a=1, b=-1, c=-2 Force if a=1, b=1, c=-2 Velocity if a=0, b=1, c=-1 All of the above The dimensions of mobility are given by: [M -1 L 0 T 2 A 1 ] [M -1 L 1 T 2 A 1 ] [M 1 L 0 T -2 A -1 ] [M 1 L 1 T -3 A -1 ] The physical quantity that has the same dimensions as 1 2 0 E 2 (where 0 is the permittivity of free space and E is the electric field) is: Pressure Force Energy Power The dimensions of Boltzmann constant are: [ML 2T -2 K -1 ] [ML 2T -2 K] [MLT -2 K -1 ] [ML 2T -1 K -1 ] The dimensions of magnetic flux are: [ML 2T -2 A -1 ] [ML 2T -1 A -1 ] [MLT -2 A -1 ] [ML 2T -2 A -2 ] The dimensional formula of self-inductance is: [ML 2T -2 A -2 ] [ML 2T -1 A -2 ] [MLT -2 A -2 ] [ML 2T -2 A -1 ] In the Van der Waals equation (P + a V 2 )(V - b) = RT , the dimensions of the constant a are: [ML 5T -2 ] [ML 3T -2 ] [M 0L 3T 0] [ML 2T -2 ] The dimensions of pressure gradient are: [ML -2 T -2 ] [ML -1 T -2 ] [ML -2 T -1 ] [M 0L -2 T -2 ] The solid angle subtended by the periphery of an area 1 cm 2 at a point on the axis of the area 5 cm away is: 4 10 -2 steradian 2 10 -1 steradian 4 10 -1 steradian 2 10 -2 steradian Dimensions of resistance in an electrical circuit, in terms of dimension of mass M , of length L , of time T and of current A , are: [ML 2T -3 A -2 ] [ML 2T -3 A -1 ] [ML 3T -3 A -2 ] [MLT -3 A -2 ] What is the dimension of the constant k in the Coulomb's law equation F = k q 1q 2 r 2 ? [ML 3T -4 A -2 ] [ML 3T -2 A -2 ] [ML 2T -4 A -2 ] [ML 3T -4 A -1 ] The dimension of the coefficient of self-induction is: [ML 2T -2 A -2 ] [ML 2T -2 A -1 ] [MLT -2 A -2 ] [ML 2T -1 A -2 ] The dimensions of electric potential are: [ML 2T -3 A -1 ] [ML 2T -2 A -1 ] [ML 1T -3 A -1 ] [ML 2T -3 A -2 ] The dimensions of Rydberg constant R are: [M 0L -1 T 0] [M 0L 1T 0] [M 1L 0T 0] [M 0L 0T 1] The dimensions of the ratio of 'Magnetic Flux' to 'Inductance' are same as that of: Current Voltage Resistance Charge Which of the following is the dimension of the Universal Gas Constant ( R )? [ML 2T -2 K -1 mol -1 ] [ML 2T -2 K -1 ] [ML 3T -2 K -1 mol -1 ] [ML 2T -3 K -1 mol -1 ] The dimensions of displacement current are: [M 0L 0T 0A 1] [M 0L 0T 1A 1] [ML 2T -2 A -1 ] [M 0L 0T -1 A 1] If the value of the Stefan-Boltzmann constant is , the dimensions of are: [ML 0T -3 K -4 ] [ML 2T -3 K -4 ] [ML 0T -2 K -4 ] [ML 2T -2 K -4 ] The dimensions of 'Hubble's Constant' are same as that of: Frequency Velocity Acceleration Force Which of the following physical quantities has the dimensions [M 0L 2T -2 ] ? Latent heat Specific heat Gravitational constant Surface tension The dimensions of 'Bohr Magneton' are: [M 0L 2T 0A 1] [M 0L 1T 0A 1] [M 1L 2T -2 A -1 ] [M 0L 2T -1 A 1] The dimensions of 'Gravitational Potential' are: [M 0L 2T -2 ] [M 1L 2T -2 ] [M 0L 1T -2 ] [M -1 L 3T -2 ] The dimensions of 'Electric Flux' are: [ML 3T -3 A -1 ] [ML 2T -3 A -1 ] [ML 3T -3 A 1] [M 0L 3T -3 A -1 ] The dimensions of 1/(LC) where L is inductance and C is capacitance are same as that of: Square of frequency Frequency Time Square of time Which of the following physical quantities has the same unit and dimensions as that of pressure? Young's modulus Surface tension Force Momentum Which of the following physical quantities is dimensionless? Relative Permeability Magnetic Permeability Permittivity of free space Electric Flux The ratio of the dimensions of L/R (where L is inductance and R is resistance) is: [T] [T -1 ] [M 0L 0T 0] [LT -1 ] The dimension of surface energy per unit area is: [MT -2 ] [ML 2T -2 ] [MLT -2 ] [ML 0T -2 ] The dimensions of molar gas constant R are: [ML 2T -2 K -1 mol -1 ] [ML 2T -2 K -1 ] [MLT -2 K -1 mol -1 ] [ML 2T -3 K -1 mol -1 ] Which of the following is the dimension of the 'intensity of wave'? [MT -3 ] [MLT -3 ] [ML 2T -3 ] [MT -2 ] The dimension of 'decay constant' of a radioactive sample is same as that of: Frequency Time Velocity Activity A force F is given by F = at + bt 2 , where t is time. The dimensions of a and b are: [MLT -3 ] and [MLT -4 ] [MLT -2 ] and [MLT 0] [MLT -1 ] and [MLT -2 ] [MLT -4 ] and [MLT -3 ] What is the dimension of gravitational potential gradient? [LT -2 ] [MLT -2 ] [L 2T -2 ] [T -2 ] Which of the following physical quantities has the dimension of [ML 2T -3 A -1 ] ? Electric Potential Resistance Electric Field Capacitance The dimensions of 'Permittivity of Free Space' 0 are: [M -1 L -3 T 4A 2] [M -1 L 3T -4 A -2 ] [ML 3T -4 A -2 ] [M -1 L -3 T 2A 2] The dimension of the ratio of 'Work' to 'Torque' is: [M 0L 0T 0] [L] [MLT -2 ] [T -1 ] The dimensions of the ratio of 'Electric Field' ( E ) to 'Magnetic Field' ( B ) are same as that of: Velocity Acceleration Force Current If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of: [M 2 L -1 T 0] [M 2 L -2 T -1 ] [M L 0 T 0] [M 0 L -1 T 1] The dimensions of 'Angular Impulse' are the same as that of: Angular momentum Linear momentum Torque Energy The physical quantity having the dimensional formula [ML -1 T -2 ] is: Young's Modulus Surface Tension Coefficient of Viscosity Solar Constant A force F is given by F = at + bt 2 , where t is time. The dimension of a/b is: [T -1 ] 建设 [T] 建设 [L] 建设 [L T -1 ] 建设 The dimensions of the ratio of 'Magnetic induction ( B )' to 'Electric field ( E )' ( B/E ) are: [L -1 T] 建设 [LT -1 ] 建设 [MT -1 ] 建设 [MLT -1 ] 建设 Which of the following physical quantities is not dimensionless? Gravitational Potential Relative Permeability Refractive Index Strain The dimensions of 'Universal Gas Constant' ( R ) per molecule is called Boltzmann constant ( k B ). Its dimensions are: [ML 2T -2 K -1 ] 建设 [ML 2T -2 ] 建设 [MLT -2 K -1 ] 建设 [ML 2T -3 K -1 ] 建设 Dimensional formula of 'Electric Field Intensity' is: [MLT -3 A -1 ] 建设 [ML 2T -3 A -1 ] 建设 [MLT -3 A] 建设 [ML 2T -3 A -2 ] 建设 If force ( F ), velocity ( V ) and time ( T ) are taken as the fundamental physical quantities, the dimensions of mass are: [FV -1 T] [FVT -1 ] [FV -2 T] [FVT] The velocity of a particle depends on time as v = at + b t+c . The dimensions of b are: [L] [LT -1 ] [LT -2 ] [T] The dimensions of the quantity 1 2 LI 2 (where L is inductance and I is current) are: [ML 2T -2 ] [MLT -2 ] [ML 2T -1 ] [ML 2T -3 ] The product of magnetic permeability ( 0 ) and electric permittivity ( 0 ) of free space has the dimensions: [L -2 T 2 ] [L 2 T -2 ] [LT -1 ] [L -1 T] The dimensions of the Poynting vector (energy flow per unit area per unit time) are: [MT -3 ] [ML 2 T -3 ] [MT -2 ] [MLT -2 ] The dimensions of electric field gradient are: [MT -3 A -1 ] [MLT -3 A -1 ] [ML 2T -3 A -1 ] [MT -2 A -1 ] The mechanical equivalent of heat ( J ) has the dimensions: [M 0 L 0 T 0 ] [ML 2 T -2 ] [L 2 T -2 ] [MLT -2 ] The dimensions of GM R (where G is universal gravitational constant, M is mass of Earth and R is radius of Earth) are: [L 2 T -2 ] [LT -2 ] [L 2 T -1 ] [ML 2 T -2 ] The dimensions of 'torque per unit twist' (torsional rigidity) are: [ML 2 T -2 ] [MLT -2 ] [ML -1 T -2 ] [M 0 L 2 T -2 ] The dimensions of 'Dynamic Pressure', given by the expression 1 2 v 2 (where is density and v is velocity), are the same as that of: Pressure Force Energy Momentum Which of the following physical quantities has the same unit as that of 'Pressure Gradient'? Newton per metre cube Pascal per metre Joule per metre square Newton per metre square The dimensions of 'Magnetic Permeability' 0 are: [MLT -2 A -2 ] [ML 2T -2 A -2 ] [MLT -2 A -1 ] [M 0L 0T 0A 0] Dimensions of 1 4 0 are: [ML 3T -4 A -2 ] [ML 2T -3 A -2 ] [M -1 L -3 T 4A 2] [ML 3T -2 A -2 ] The dimension of the ratio of 'Potential Difference' to 'Current' is same as that of: Resistance Conductance Inductance Capacitance The dimensions of 'Coefficient of Mutual Inductance' are: [ML 2T -2 A -2 ] [ML 2T -1 A -2 ] [MLT -2 A -2 ] [ML 2T -2 A -1 ] The dimensions of 'Potential Gradient' are: [MLT -3 A -1 ] [ML 2T -3 A -1 ] [MLT -2 A -1 ] [M 0L 0T 0] The dimensions of 'Modulus of Rigidity' (or Shear Modulus) are: [ML -1 T -2 ] [ML -2 T -2 ] [MLT -2 ] [ML 2T -2 ] The dimensions of B 2 2 0 (Magnetic Energy Density) are: [ML -1 T -2 ] [ML 2T -2 ] [MLT -2 ] [ML -2 T -1 ] In a calculation y = A (Bt - Cx) , the dimensions of B/C are the same as that of: Velocity Frequency Wavelength Time Which of the following has the dimension of [ML 2T -2 ] ? Moment of force Moment of momentum Moment of inertia Moment of mass The dimensions of 'Surface Energy' are: [MT -2 ] [ML 2T -2 ] [MLT -2 ] [MT -1 ] Dimensions of the quantity L/C where L is inductance and C is capacitance are same as that of: Resistance Frequency Time Current If the units of mass, length and time are doubled, the unit of angular momentum will be: 8 times 4 times 2 times 16 times Dimensions of 'Electric Polarisation' (dipole moment per unit volume) are: [L -2 T A] [L -3 T A] [M L -2 T A] [L 2 T -1 A] The dimensions of the constant b in the Wien's Displacement Law ( max T = b ) are: [LK] [L -1 K] [LK -1 ] [L 0K] In the equation y = a ( t - kx) , the dimension of /k is same as that of: Velocity Acceleration Wavelength Time The dimension of 0 E 2 (where 0 is permittivity and E is electric field) is that of: Pressure Force Power Linear momentum If velocity ( V ), force ( F ) and energy ( E ) are taken as fundamental units, then dimensions of mass will be: [EV -2 ] [FV -2 ] [FV -1 T 0] [EV -1 ] If L , C and R represent inductance, capacitance and resistance respectively, which of the following combinations does not have the dimensions of frequency? R/L 1/RC 1/ LC C/L Which of the following physical quantities has the same dimensions as that of 'Energy Density'? Modulus of Elasticity Force Angular Momentum Power The dimension of 'Magnetic Susceptibility' is: [M 0L 0T 0] [M 0L 1T 0] [M 0L 0T -1 ] [M 1L 0T 0] The dimensions of 'Molar Heat Capacity' ( C m ) are: [ML 2T -2 K -1 mol -1 ] [ML 2T -2 K -1 ] [ML 2T -3 K -1 mol -1 ] [L 2T -2 K -1 mol -1 ] The dimension of [M 1 L 2 T -2 A -2 ] corresponds to: Inductance Resistance Capacitance Magnetic Flux The dimensions of [ML -2 T -2 ] are those of: Force gradient Pressure gradient Stress Energy gradient The dimensions of [ML 2T -3 A -1 ] are: Electric Field Intensity Electric Potential Resistance Magnetic Flux The dimension of the ratio of 'Work' to 'Time' is: [ML 2T -3 ] [ML 2T -2 ] [MLT -2 ] [ML 2T -1 ] The dimension of the ratio of 'Magnetic Flux' to 'Time' is same as that of: Electromotive Force Resistance Current Electric Field The dimensions of 'Intensity of Magnetization' (magnetic moment per unit volume) are: [M 0 L -1 T 0 A 1] [M 0 L 2 T 0 A 1] [M 1 L -1 T -2 A 0] [M 0 L -2 T 0 A 1] If the units of length, mass, and time are each increased by a factor of 10 , the unit of force will increase by a factor of: 1 10 100 1000 If P, Q, R are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity? (P - Q) / R PQ / R PQ - R (P + Q) R The dimensional formula for 'Electric Conductivity' is: [M -1 L -3 T 3 A 2] [M 1 L 3 T -3 A -2 ] [M -1 L 3 T -3 A 2] [M 1 L -3 T 3 A -2 ] The dimensions of 'Magnetic field' ( B ) in terms of M, L, T and A (current) are: [M 1 L 0 T -2 A -1 ] [M 1 L 1 T -2 A -1 ] [M 1 L 0 T -1 A -2 ] [M 0 L 2 T -2 A -1 ] The dimensions of 'Solar Constant' are same as those of: Intensity of wave Pressure Force Energy Density The dimensions of 'Capacitance' in terms of M, L, T and A are: [M -1 L -2 T 4 A 2] [M 1 L 2 T -4 A -2 ] [M -1 L -2 T 2 A 2] [M 0 L -2 T 4 A 2] In the equation v = a + bt + c/(d+t) , where v is velocity and t is time, the dimensions of c are: [L] [LT -1 ] [LT -2 ] [T] Which of the following physical quantities has the same dimensions as that of the expression h mc , where h is Planck's constant, m is mass and c is velocity of light? Length Time Mass Velocity The dimension of the quantity 1/( 0 0) is: [L 2T -2 ] [L T -1 ] [L 2T 2 ] [L -2 T 2 ] The dimension of the product of 'Stress' and 'Strain' is equivalent to the dimension of: Energy per unit volume Force per unit area Work per unit length Power In a system of units, if Force ( F ), Acceleration ( A ), and Time ( T ) are taken as fundamental units, then the dimensional formula of 'Energy' is: [FAT] [FA 2T] [FAT 2] [F 2AT] The dimensions of 'Compressibility' are: [M -1 LT 2] [ML -1 T -2 ] [MLT -2 ] [M 0L 0T 0] If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system? 10 5 kg 10 3 kg 10 4 kg 10 6 kg What is the dimension of 'Magnetic Field Intensity' ( H )? [L -1 A] [LA] [L 2A] [MLT -2 A -1 ] The dimension of 1 2 0 E 2 (Energy Density) is same as that of: Pressure Force Energy Power The dimensions of the quantity [ML 2T -2 K -1 ] correspond to: Boltzmann Constant Stefan-Boltzmann Constant Universal Gas Constant Thermal Conductivity Which of the following pairs has different dimensions? Moment of inertia and Moment of force Work and Torque Angular momentum and Planck's constant Impulse and Linear momentum The dimensions of 'Solar Constant' (Energy received per unit area per unit time) are: [MT -3 ] 联合 [ML 2T -3 ] 联合 [MLT -2 ] 联合 [MT -2 ] 联合 The dimensions of 'Magnetic Permeability' ( 0 ) are: [MLT -2 A -2 ] 联合 [ML 2T -2 A -2 ] 联合 [MLT -2 A -1 ] 联合 [ML 2T -2 A -1 ] 联合 The dimension of the ratio of 'Torque' to 'Angular Acceleration' is: [ML 2] [ML 2T -2 ] [MLT -1 ] [M 0L 0T 0] The dimensions of 'Angular Momentum' are: [ML 2T -1 ] 联合 [ML 2T -2 ] 联合 [MLT -1 ] 联合 [MLT -2 ] 联合 The dimensions of 'Coefficient of Viscosity' are: [ML -1 T -1 ] 联合 [ML -1 T -2 ] 联合 [MLT -1 ] 联合 [ML 2T -1 ] 联合 The dimensional formula for the 'Electric Displacement Field' ( D ) is given by: [M 0 L -2 T 1 A 1] [M 1 L -2 T 1 A 1] [M 0 L -3 T 1 A 1] [M 0 L -2 T -3 A 1] The dimensions of the 'Torsional Constant' ( k ) of a wire, defined by the torque = k , are: [M 1 L 2 T -2 ] [M 1 L 1 T -2 ] [M 1 L 2 T -1 ] [M 1 L 0 T -2 ] The dimensions of 'Angular Velocity Gradient' are: [M 0 L -1 T -1 ] [M 0 L 0 T -1 ] [M 0 L 0 T -2 ] [M 0 L -1 T -2 ] If Force ( F ), Length ( L ), and Time ( T ) are taken as the fundamental physical quantities, the dimensional formula for 'Mass' will be: [F 1 L -1 T 2] [F 1 L 1 T -2 ] [F 1 L -1 T -2 ] [F 1 L 1 T 2] The dimensions of 'Electric Displacement Current Density' ( J d ) are: [M 0 L -2 T 0 A 1] [M 0 L -2 T -1 A 1] [M 0 L -1 T 0 A 1] [M 0 L -3 T 0 A 1] If the dimensions of a physical quantity are given by M a L b T c I d , where I represents electric current, the quantity is 'Conductivity' if: a = -1, b = -3, t = 3, d = 2 a = 1, b = 3, t = -3, d = -2 a = -1, b = -3, t = -3, d = 2 a = 0, b = -2, t = 3, d = 2 Which of the following physical quantities has the same dimensions as that of 'Planck's constant' divided by 'Electronic charge' ( h/e )? Magnetic Flux Magnetic Induction Electric Potential Electric Flux The dimension of the quantity L 2 / (m r 4 2) (where L is angular momentum, m is mass, r is radius and is angular velocity) is: [M 1 L 0 T 0] [M 0 L 0 T 0] [M L 2 T -2 ] [M 2 L 2 T -1 ] The dimension of the quantity 1/( 0 E 2) where E is the electric field is that of: Inverse of pressure Pressure Energy Force The dimensions of 'Radiation Pressure' are: [ML -1 T -2 ] 联合 [MLT -2 ] 联合 [ML 2T -3 ] 联合 [M 0L 0T 0] 联合 The dimension of the quantity G g (where G is universal gravitational constant and g is acceleration due to gravity) is: [M -1/2 L 1 ] [M 1/2 L -1 ] [M L T -2 ] [L] In a system of units, the unit of power is 100 W, the unit of force is 10 N, and the unit of time is 10 s. The unit of mass in this system is: 10 kg 100 kg 1 kg 0.1 kg What are the dimensions of 'Action'? [ML 2T -1 ] [ML 2T -2 ] [MLT -1 ] [ML 2T 0] The dimensions of 'Thermal Conductivity' k in terms of mass M , length L , time T and temperature are: [MLT -3 -1 ] [ML 2T -3 -1 ] [MLT -2 -1 ] [M 1L 2T -2 -1 ] The dimension of 'Magnetic Pole Strength' in the SI system is given by: [M 0L 1T 0A 1] [M 0L 0T 0A 1] [M 1L 1T -2 A -1 ] [M 0L 2T 0A 1] The dimensions of 'Specific Heat Capacity' in terms of M, L, T and are: [M 0L 2T -2 -1 ] [M 1L 2T -2 -1 ] [M 0L 2T -1 -1 ] [M 1L 1T -2 -1 ] The dimensions of the 'Stefan-Boltzmann Constant' in terms of M, T and are: [MT -3 -4 ] [ML 2T -3 -4 ] [MT -2 -4 ] [ML 0T -3 -4 ] Which of the following physical quantities has the dimensional formula [M 1L 2T -3 A -2 ] ? Resistance Resistivity Conductance Inductance The dimensions of 'Universal Gas Constant' R in terms of M, L, T, and number of moles mol are: [ML 2T -2 -1 mol -1 ] [ML 2T -2 -1 ] [ML 2T -3 -1 mol -1 ] [ML 2T -2 mol -1 ] The dimensions of 'Magnetic Induction' B in terms of M, T and Charge Q are: [MT -1 Q -1 ] [MLT -1 Q -1 ] [MT -2 Q -1 ] [MT 1Q -1 ] If the dimensions of a physical quantity are [M a L b T c] , then it represents velocity if: a=0, b=1, c=-1 a=1, b=1, c=-1 a=0, b=1, c=-2 a=1, b=0, c=-1 Which of the following constants has the same dimensions as that of 'Torque per unit twist'? Work Angular Momentum Force Young's Modulus In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X= A 2B 1/2 C 1/3 D 3 , will be 10% ( 3 13 ) % 16% – 10% A metal wire has mass (0.4 0.002) g, radius (0.3 0.001) mm and length (5 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be 1.2% 1.3% 1.6% 1.4% Each side of a metallic cube of mass 5.580 kg is measured to the 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X 10 3 kg m -3 where the value of X is: 7.654 7.7 7.65 7.6 The density of a material in CGS system of units is 4 g/cm 3 . In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be: 40 400 0.04 0.4 The dimensional formula of magnetic permeability is: [MLT -2 A -2 ] [ML 2T -2 A -1 ] [MLT -1 A -2 ] [ML 2T -2 A -2 ] The dimensions of Stefan-Boltzmann constant are: [MT -3 K -4 ] [ML 2T -3 K -4 ] [MLT -3 K -4 ] [M 2T -3 K -4 ] A quantity X is given by 0 L V t , where 0 is permittivity of free space, L is a length, V is potential difference and t is time interval. The dimensional formula for X is same as that of: Current Resistance Voltage Capacitance A physical quantity of the dimensions of length that can be formed out of c , G and e 2 4 0 is [ c is velocity of light, G is universal constant of gravitation and e is charge]: 1 c 2 [G e 2 4 0 ] 1/2 c 2 [G e 2 4 0 ] 1/2 1 c 2 G e 2 4 0 1 c G e 2 4 0 The dimensions of Thermal Resistance are: [M -1 L -2 T 3K] [ML 2T -3 K -1 ] [ML 2T -2 K -1 ] [M -1 L -2 T 3K -1 ] The dimensions of the quantity 'Resistance' 'Capacitance' ( RC ) are same as that of: Time Frequency Velocity Force What are the dimensions of the 'impedance of free space' (given by 0/ 0 )? [ML 2T -3 A -2 ] [ML 3T -3 A -2 ] [M 0L 0T 0A 0] [ML 2T -2 A -1 ] What is the dimension of the ratio of 'magnetic field' ( B ) to 'magnetic intensity' ( H ) in vacuum? [MLT -2 A -2 ] [ML 2T -2 A -1 ] [M 0L 0T 0] [MLT -2 A -1 ] The dimensional formula of 'resistivity' in terms of M, L, T and Q (where Q is charge) is: [ML 3T -1 Q -2 ] [ML 2T -1 Q -2 ] [ML 3T -1 Q -1 ] [ML 3T -2 Q -2 ] The dimensions of the electrical conductivity are: [M -1 L -3 T 3A 2] [M -1 L -3 T 3A 1] [ML 3T -3 A -2 ] [M -1 L -2 T 3A 2] The dimensions of 'Action' (as in Principle of Least Action) are same as that of: Angular momentum Linear momentum Force Energy The dimension of [ML 2T -2 A -2 ] corresponds to: Magnetic permeability Electric permittivity Self inductance Magnetic flux The dimensional formula for 'Faraday constant' ( F = N A e ) is: [M 0L 0TA] 建设 [MLT -1 A] 建设 [M 0L 0T -1 A] 建设 [M 0L 0T 0A] 建设 The dimension of the expression L/C is same as that of: Resistance Conductance Frequency Time If the velocity of light c , Planck's constant h and gravitational constant G are taken as fundamental quantities, then the dimensions of 'Mass' will be: [c 1/2 h 1/2 G -1/2 ] 建设 [c 1/2 h 1/2 G 1/2 ] 建设 [c 3/2 h 1/2 G -1/2 ] 建设 [c 5/2 h 1/2 G -1/2 ] 建设 The dimensions of the quantity 0 / 0 are: [M -1 L -2 T 3A 2] 建设 [ML 2T -3 A -2 ] 建设 [M 0L 0T 0A] 建设 [MLT -3 A -1 ] 建设 Which of the following physical quantities is dimensionless? Relative Permeability Magnetic Flux Electric Potential Inductance If energy ( E ), velocity ( V ) and time ( T ) are chosen as the fundamental quantities, the dimensional formula of surface tension is: [EV -2 T -2 ] [EV -1 T -2 ] [E -2 V -1 T] [EV -2 T -1 ] The pressure P of a gas depends on distance x and time t as P = a - x 2 bt . The dimensions of a b are: [ML -1 T -1 ] [M 0 L 2 T -1 ] [ML 3 T -1 ] [M -1 L 1 T 2 ] The dimensional formula for the quantity L RC (where L is inductance, R is resistance, and C is capacitance) is the same as that of: Resistance Voltage Current Time The dimension of the ratio of 'Magnetic Flux' to 'Resistance' is same as that of: Electric Charge Electric Current Electric Potential Inductance If P = a - t 2 bx where P is pressure, x is distance and t is time, then the dimensions of a/b are: [ML 2T -2 ] [MLT -2 ] [M 2L -1 T -3 ] [ML -1 T -2 ] The dimension of 'Electric Capacitance' is: [M -1 L -2 T 4A 2] [ML 2T -3 A -1 ] [M -1 L -2 T 2A 2] [ML 2T -4 A -2 ] Which of the following is the dimensional formula for 'Conductance'? [M -1 L -2 T 3A 2] [ML 2T -3 A -2 ] [M -1 L -2 T 3A 1] [ML 2T -3 A -1 ] If Planck's constant ( h ), speed of light ( c ) and gravitational constant ( G ) are used to form a unit of length, which of the following is the correct expression? hG c 3 hc G hG c 3/2 G hc 3 The dimensions of polarizability defined by p = E (where p is dipole moment and E is electric field) are: [M -1 L 0 T 4 A 2] [M 0 L 3 T 0 A 0] [M -1 L 2 T 3 A 1] [M 1 L 3 T -4 A -2 ] The dimensions of the constant in the relation F = Density are: [M 1/2 L 3/2 T -2 ] [M 3/2 L 1/2 T -2 ] [M 1 L 2 T -2 ] [M 1/2 L -3/2 T -2 ] The dimension of [ML 2T -3 ] corresponds to: Power Work Force Energy If the dimensions of length are expressed as G x c y h z , where G is the universal gravitational constant, c is the speed of light and h is Planck's constant, then the values of x, y and z are respectively: 1/2, -3/2, 1/2 1/2, 3/2, 1/2 1/2, -3/2, -1/2 -1/2, -3/2, 1/2 The dimensions of [ 0 E] (where 0 is permittivity of free space and E is electric field) are same as that of: Electric Displacement ( D ) Electric Flux Electric Potential Current Density The dimensions of 'Electric Quadrupole Moment' are: [L 2TA] [LTA] [L 2A] [L 2T 2A] The dimensions of the quantity 1 2 0 H 2 (where 0 is magnetic permeability and H is magnetic field intensity) are same as that of: Pressure Force Power Angular Momentum The units of 'Surface Tension' in SI system are N/m . In a new system of units, the unit of mass is 10 kg, length is 10 m and time is 100 s. The numerical value of surface tension 1 N/m in the new system is: 1000 100 10 0.1 The dimension of h e (where h is Planck's constant and e is electronic charge) is same as that of: Magnetic Flux Electric Field Magnetic Induction Electric Flux The dimensions of the quantity hG c 5 are same as that of: Time Length Mass Energy In the formula X = 3YZ 2 , X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in SI units? [M -3 L -2 T 8A 4] [M -3 L -2 T 4A 4] [M -2 L -2 T 4A 4] [M -1 L -2 T 4A 2] In a system where speed of light ( c ), gravitational constant ( G ), and Planck's constant ( h ) are taken as fundamental units, the dimensions of 'Time' would be: Gh/c 5 Gc/h 3 hc/G Gh/c 3 The dimensions of 'Electrical Permittivity' ( 0 ) are: [M -1 L -3 T 4A 2] 联合 [M 1L -3 T 4A 2] 联合 [M -1 L 3 T -4 A -2 ] 联合 [M -1 L -3 T 2A 1] 联合 If the units of length and force are increased four times, then the unit of energy will: Increase 16 times Increase 8 times Increase 4 times Remain unchanged The dimension of the ratio of 'Magnetic Flux' to 'Resistance' is same as that of: Charge Current Potential Inductance The dimensions of the quantity R C L (where R is resistance, C is capacitance, and L is inductance) are: [M 0 L 0 T 0] [T 1] [T -1 ] [M 1 L 2 T -3 A -2 ] The dimensions of 'Magnetic Vector Potential' ( A ), defined such that the magnetic field B = A , are: [M 1 L 1 T -2 A -1 ] [M 1 L 2 T -2 A -1 ] [M 1 L 0 T -2 A -1 ] [M 0 L 1 T -2 A -1 ] The dimension of the quantity R 2 C (where R is resistance and C is capacitance) is: [M 1 L 2 T -1 A -2 ] [M 1 L 2 T -3 A -2 ] [T 2] [M 0 L 0 T 1] The dimensions of 'Illuminance' (unit Lux), defined as luminous flux incident per unit area, are: [M 1 L 0 T -3 ] [M 1 L 2 T -3 ] [M 0 L -2 T 0] [M 1 L -2 T -3 ] The dimensions of 'Molar Entropy' are: [M 1 L 2 T -2 K -1 mol -1 ] [M 1 L 2 T -2 K -1 ] [M 0 L 0 T 0 K -1 mol -1 ] [M 1 L 1 T -2 K -1 mol -1 ] The dimensions of 'Thermal Diffusivity' (defined as thermal conductivity divided by the product of density and specific heat capacity) are: [L 2 T -1 ] [L 2 T -2 ] [ML 2 T -1 ] [L T -1 ] The dimensions of 'Gravitational Constant' ( G ) in terms of 'Planck's constant' ( h ), 'Velocity of light' ( c ) and 'Mass' ( m ) is given by: [h 1 c 1 m -2 ] [h 0 c 1 m -1 ] [h -1 c 1 m 2] [h 1 c -1 m -2 ] What are the dimensions of 1 B 0 0 where B is magnetic field? [L 2 I -1 ] [L 2] [T 2 I] [M L 2 T -2 ] The dimensions of 'Magnetic Dipole Moment' in terms of M, L, T and 'Potential Difference' ( V ) are: [M L 2 T -1 V -1 ] [M 0 L 2 T 0 V 0] [L 3 T -1 V] [M L 2 T -2 V -1 ] The dimensions of 'Surface Tension' are same as that of: Spring constant Pressure Stress Modulus of elasticity In a system of units, if M, L, T are the fundamental units, the dimensional formula for 'Electric Charge' in terms of M, L, T and 'Potential Difference' V is: [M -1 L -2 T 2V 1] [M 1L 2T -2 V -1 ] [M 1L 1T -1 V 1] [M 0L 0T 0V 1] The unit of 'Equivalent Dose' of radiation in the SI system is 'Sievert' ( Sv ). Its dimensional formula is: [L 2T -2 ] [ML 2T -2 ] [L 2T -3 ] [ML 2T -3 ] The dimension of 'Magnetic Flux' in terms of M, L, T and Charge Q is: [ML 2T -1 Q -1 ] [ML 2T -2 Q -1 ] [MLT -1 Q -1 ] [ML 2Q -2 ] The dimension of 'Self-Inductance' in terms of M, L, T and Charge Q is: [ML 2Q -2 ] [ML 2T -1 Q -2 ] [ML 2T -2 Q -2 ] [MLQ -2 ] The dimensions of 'Capacitance' in terms of M, L, T and Charge Q are: [M -1 L -2 T 2Q 2] [ML 2T -2 Q -2 ] [M -1 L -2 T 0Q 2] [ML 2Q -2 ] The dimensions of 'Coefficient of Viscosity' can be expressed as: Pressure Time Force Time Energy Time Force / Time The dimensions of 'Luminous Flux' (measured in Lumens) in terms of M, L, T are: [ML 2T -3 ] [ML 2T -2 ] [MLT -3 ] [MT -3 ] Consider that s , k B , b represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of s k B -1 b is [ L -1 T -1 K -2 ] [ L -1 K -2 ] [ L -1 T -1 K -3 ] [ L -1 T -1 K -4 ] Dimensions of 'Kinetic Energy' are same as that of: Torque Force Momentum Power The dimensions of 'Heat Capacity' of a body are: [M 1 L 2 T -2 K -1 ] [L 2 T -2 K -1 ] [M 1 L 1 T -2 K -1 ] [M 1 L 2 T -3 K -1 ] The dimensions of [M 1 L -1 T -2 ] represent: Bulk Modulus Surface Tension Force Torque Which of the following methods is most suitable for measuring the distance of a star that is less than 100 light-years away? Parallax method Reflection method Direct measurement with a meter scale Echo method The dimensions of Young's Modulus of elasticity are: [ML -1 T -2 ] [ML 1T -2 ] [ML -1 T -1 ] [ML 2T -2 ] The dimension of the ratio of 'Magnetic Flux' to 'Time' is equivalent to the dimension of: Electric Potential Electric Current Resistance Capacitance In the equation of a wave, y = A (kx - t + ) , the dimensions of the phase constant are: [M 0 L 0 T 0] [L 1] [T 1] [L -1 ] The dimensions of 'Specific Volume' (volume per unit mass) are: [M -1 L 3 T 0] [M 1 L -3 T 0] [M 0 L 3 T 0] [M -1 L 2 T 0] Which of the following physical quantities has the dimension of [M 1 L 2 T -3 ] ? Power Work Force Pressure A force F is defined by F = at + bt 2 , where t is time. What are the dimensions of a and b ? [MLT -3 ] and [MLT -4 ] [MLT -2 ] and [MLT -3 ] [MLT -1 ] and [MLT -2 ] [ML 2T -3 ] and [ML 2T -4 ] The volume of a liquid flowing out per second through a pipe of length l and radius r is V = P r 4 8 l , where P is pressure difference and is coefficient of viscosity. The dimensions of V are: [L 3 T -1 ] [L 3 T] [L 2 T -1 ] [M L 3 T -1 ] The dimensions of 'Entropy' are: [ML 2T -2 K -1 ] [ML 2T -2 ] [MLT -2 K -1 ] [M 2L 2T -2 K -1 ] The dimensions of 'Mutual Inductance' are the same as those of: Self Inductance Resistance Capacitance Magnetic Flux The dimension of 'Magnetic Dipole Moment' in terms of M, L, T and A is: [L 2A] [L 2TA] [L 1A] [ML 2T -1 A] If L is the inductance and R is the resistance, then the dimensions of L/R are: [T] [T -1 ] [M 0 L 0 T 0] [L/T] Which of the following constants has the dimension [ML 2T -1 ] ? Planck's constant Gravitational constant Stefan's constant Gas constant The dimensions of 'Specific Heat Capacity' are: [L 2 T -2 K -1 ] [M L 2 T -2 K -1 ] [L 2 T -2 ] [M L T -2 K -1 ] The dimensions of the quantity 1/RC (where R is resistance and C is capacitance) are the same as that of: Frequency Time Velocity Acceleration The dimensions of 'Surface Tension' in terms of Force F and length L are: [FL -1 ] [F 1L 1] [FL -2 ] [F 0L 0] The dimensions of 'Electric Dipole Moment' p in terms of M, L, T and current A are: [M 0L 1T 1A 1] [M 0L 1T 0A 1] [M 1L 1T -1 A 1] [M 0L 2T 0A 1] The dimensions of potential energy U are the same as that of: Torque Force Momentum Power The dimensions of the ratio of electric field E to magnetic field B ( E/B ) are: [LT -1 ] [L -1 T] [M 0L 0T 0] [MLT -3 A -1 ] The dimensions of ( 0 0) -1/2 are: [LT -1 ] [L 1/2 T -1/2 ] [L -1 T] [MLT -1 ] The dimensions of torque are: [ML 2T -2 ] Hastings [MLT -2 ] [ML 2T -1 ] [MLT -1 ] Which of the following physical quantities is represented by the dimensional formula [M 1 L -1 T -2 ] ? Bulk Modulus Surface Tension Viscosity Moment of Inertia The dimensions of the time constant RC are: [M 0L 0T 1] [M 0L 0T -1 ] [ML 2T -3 A -2 ] [ML 2T -3 A -1 ] Dimensions of 'Wien's Constant' b are: [M 0L 1T 0K 1] [M 0L 1T 0K -1 ] [M 1L 1T -3 K -1 ] [M 0L 0T 0K 1] The dimensions of the 'Force Constant' of a spring are: [M 1L 0T -2 ] [M 1L 1T -2 ] [M 1L 0T -1 ] [M 0L 0T -2 ] Which of the following physical quantities is dimensionless? Reynolds Number Gravitational Constant Planck Constant Gas Constant The dimensions of 'coefficient of linear expansion' are: [K -1 ] [LK -1 ] [ML 0T 0K -1 ] [L 0K] The dimension of stress is: [ML -1 T -2 ] [MLT -2 ] [ML 2T -2 ] [ML 0T -2 ] The dimensions of 'Work Function' are same as that of: Energy Power Force Potential Gradient The dimensions of latent heat are: [M 0L 2T -2 ] tube [ML 2T -2 ] tube [MLT -2 ] tube [ML 2T -1 ] tube The dimensions of electric dipole moment are: [LTA] [L 2TA] [MLTA] [LT -1 A] The dimensions of magnetic dipole moment are: [L 2A] [L 2T -1 A] [LA] [L 2T A] Which of the following dimensions will be the same as that of time? L/R C/L LC R/L The dimension of the de Broglie wavelength = h/mv is: [L] [L 2] [MLT -1 ] [T] The dimensions of angular acceleration are: [T -2 ] [LT -2 ] [L 0T -1 ] [MLT -2 ] The dimensions of 1/RC are same as that of: frequency time capacitance resistance The dimensions of 'Relative Density' are: [M 0L 0T 0] [ML -3 ] [M 1L 0T 0] [M 0L -3 T 0] The dimensions of 'Impulse' are same as that of: Linear Momentum Angular Momentum Force Torque The dimensions of the quantity 1 2 0 E 2 are those of: Energy density Energy Pressure gradient Force Dimensions of impulse are: [MLT -1 ] [MLT -2 ] [ML 2T -1 ] [M 2LT -1 ] What is the dimensional formula of the 'Moment of Inertia'? [ML 2T 0] 建设 [MLT -2 ] 建设 [ML 2T -1 ] 建设 [M 0L 2T 0] 建设 The dimensional formula for 'Power' is: [ML 2T -3 ] 建设 [ML 2T -2 ] 建设 [MLT -2 ] 建设 [ML -1 T -2 ] 建设 The dimensional formula for Reynolds Number is: [M 0 L 0 T 0 ] [MLT -1 ] [ML -1 T -1 ] [M 0 L 1 T 0 ] A physical quantity y = a e -bt , where t is time. The dimensions of b are: [T -1 ] [T 1] [L 0 T 0] [M 1 L 0 T -1 ] Which of the following physical quantities has the same dimensions as that of the Bohr radius? Length Area Time Velocity The dimensions of angular velocity ( ) are: [T -1 ] [LT -1 ] [ML 2T -1 ] [T] The dimensions of current density ( J ) are: [AL -2 ] [AL 2 ] [A L -3 ] [M 0 L 0 T 0 A] In Bernoulli's equation, the term 'velocity head' is given by v 2 2g . Its dimensions are: [L] [LT -1 ] [L 2T -2 ] [T] Which of the following is a dimensionless quantity? Relative density Strain Refractive index All of these Magnetic susceptibility is a: Dimensionless quantity Quantity with dimensions [L -1 ] Quantity with dimensions [A] Quantity with dimensions [M] Inductive reactance ( X L ) has the same dimensions as: Resistance Inductance Capacitance Frequency The dimensions of gravitational field intensity at a point are the same as that of: Acceleration Force Pressure Energy By using dimensional analysis, the conversion factor from Joules to ergs is found to be: 10 7 10 5 10 -7 10 3 The dimensions of surface tension are: [ML 0T -2 ] [MLT -2 ] [ML 2T -2 ] [MT -1 ] The dimensions of the ratio of 'Planck's constant' to 'Linear Momentum' are the same as that of: Length Time Velocity Mass Which of the following pairs has the same dimensions? Work and Torque Force and Pressure Energy and Momentum Angular Momentum and Linear Momentum The physical quantity having the same dimensions as the 'Fine Structure Constant' (which is dimensionless) is: Refractive Index Specific Heat Capacity Universal Gas Constant Boltzmann Constant The dimensions of 'Gravitational Field' at a point are: [LT -2 ] [MLT -2 ] [ML 2T -2 ] [M 0L 0T 0] Dimensions of 'Mass per unit length' are: [ML -1 T 0] [ML -2 T 0] [MLT -1 ] [ML -3 T 0] If x = a + bt + ct 2 where x is in metres and t is in seconds, the unit of c is: m/s 2 m/s m s m The dimensions of 'Relative Permittivity' (Dielectric Constant) are: [M 0L 0T 0A 0] [M -1 L -3 T 4A 2] [ML 3T -4 A -2 ] [M 0L 0T 0] The dimensions of electric susceptibility e are: [M 0 L 0 T 0 A 0] [M 1 L -2 T 2 A 1] [M 0 L 1 T 1 A 1] [M -1 L 2 T 0 A -1 ] The dimension of the ratio of angular momentum to linear momentum is: [L] [ML] [TL -1 ] [M 0L 0T 0] Which of the following physical quantities has the same dimensions as the 'Product of Pressure and Volume'? Energy Force Power Momentum The dimensions of 1 0 0 are same as that of: Velocity Acceleration Force Energy The dimensional formula for 'Electric Potential Difference' is: [M 1 L 2 T -3 A -1 ] [M 1 L 1 T -3 A -1 ] [M 1 L 2 T -2 A -1 ] [M 1 L 2 T -3 A -2 ] The dimensions of the ratio of magnetic field B to electric field E ( B/E ) are: [L -1 T] [LT -1 ] [M 1L 1T -1 ] [A -1 T] Dimensions of 'Current Density' are: [M 0 L -2 T 0 A 1] [M 0 L 2 T 0 A 1] [M 0 L -3 T 0 A 1] [M 1 L -2 T 0 A 1] Which of the following represents the correct dimensions of the coefficient of thermal expansion? [K -1 ] [L K -1 ] [M L 0 T 0 K -1 ] [L -1 K -1 ] The dimensions of 'Solar Luminosity' (total power radiated by the Sun) are: [ML 2T -3 ] [ML 2T -2 ] [MLT -3 ] [ML 0T -3 ] The dimensions of 'Planck Length' are: [M 0 L 1 T 0] [M 1/2 L 3/2 T -1 ] [M 1 L 1 T -1 ] [M 0 L 1 T -1 ] In an experiment four quantities a , b , c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows : P= a 3b 2 cd % error in P is 14% 10% 7% 4% Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m? 9.98 m 9.980 m 9.9 m 9.9801 m The area of a rectangular field (in m 2 ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is 1382 1382.5 14 10 2 138 10 1 The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are Instrumental errors Personal errors Least count errors Random errors A physical quantity P is related to four observations a , b , c and d as follows: P = a 3 b 2 c d The percentage errors of measurement in a , b , c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is 15% 10% 2% 13%