Work & Kinetic Energy Theorem — Practice Questions

Free NEET Physics multiple-choice questions on Work & Kinetic Energy Theorem. Attempt each question and reveal the answer with a full explanation.

A force F = (5 i + 3 j + 2 k ) N is applied over a particle which displaces it from its origin to the point r = (2 i - j ) m. The work done on the particle in joules is: 7 10 13 5 A block of mass m is sliding down a smooth hemispherical bowl of radius R . If it starts from rest at the rim, the power delivered by the normal reaction force when the block has reached an angular position from the vertical is: Zero mg 2gR mg gR mg 2gR(1- ) A particle moves along the x-axis from x=0 to x=5 m under the influence of a force given by F = 7 - 2x + 3x 2 . The work done in the process is: 135 J 70 J 190 J 270 J A body of mass 2 kg is moving in a straight line such that its displacement s varies with time t as s = t 3 . The work done by the net force in the first 2 seconds is: 144 J 72 J 36 J 288 J A block of mass m is placed on the horizontal floor of a truck. The coefficient of static friction between the block and the floor is . The truck accelerates with an acceleration a < g . The work done by the static friction on the block when the truck moves a distance s relative to the ground is: mas Zero mgs ( g - a)ms The potential energy U of a particle as a function of its position x is shown in the graph. The force acting on the particle is positive in the region: Where the slope of the curve is negative Where the slope of the curve is positive Where the curve is a horizontal line In all regions where U > 0 For a particle projected at an angle with the horizontal with velocity u , the instantaneous power delivered by gravity at time t is: mg(gt - u ) -mg(u ) mg u -mg(u - gt) A force F = (3t) i N acts on a particle of mass 2 kg initially at rest. The work done by the force in the first 2 seconds is: 9 J 18 J 6 J 12 J A block of mass m is pushed against a horizontal spring of constant k by a distance x 0 and then released. The surface is rough with coefficient of friction . The kinetic energy of the block when it passes through the natural length of the spring is: 1 2 kx 0 2 - mgx 0 1 2 kx 0 2 + mgx 0 mgx 0 - 1 2 kx 0 2 1 2 kx 0 2 A man of mass M stands on a platform of mass m which is being pulled up by a cable with an acceleration a . The work done by the normal force between the man and the platform in time t is (starting from rest): 1 2 M(g+a)at 2 1 2 Mgat 2 M(g+a)at 2 1 2 M(g-a)at 2 A force F = -k(y i + x j ) , where k is a positive constant, acts on a particle moving in the xy -plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a) . The total work done by the force is: -ka 2 ka 2 -2ka 2 zero A potential energy curve U(x) is shown in the figure. At which point is the magnitude of the force acting on the particle maximum? The point where the slope is steepest The point where U(x) is minimum The point where U(x) is maximum The point where the curve crosses the x-axis A force F = (kx) i acts on a particle, where k is a positive constant. The work done by this force in displacing the particle from x = a to x = 2a is: 3 2 ka 2 1 2 ka 2 ka 2 2ka 2 The work done by a force F = (x 2 i + y 2 j ) N in moving a particle from (1, 2) m to (2, 3) m is: 26/3 J 13/3 J 7 J 15 J An object of mass 10 kg is projected up a rough inclined plane of 30 with a velocity of 10 m/s. It comes to rest after traveling 5 m up the plane. The work done by friction is: (Take g = 10 m/s 2 ) -250 J 250 J -500 J -750 J A bullet hits a target and loses half of its velocity after penetrating 3 cm. How much further will it penetrate before coming to rest? (Assume constant resistance) 1 cm 2 cm 3 cm 0.5 cm A body of mass 2 kg is moving with a momentum of 10 kg m/s. A force of 0.5 N acts on it in the direction of motion for 2 seconds. The final kinetic energy is: 30.25 J 25 J 27.5 J 32 J A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 1 3 t 2 , where t is in seconds. Work done by the force in 2 seconds is:- 5 19 J 3 8 J 8 3 J 19 5 J A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is mg(h + d) - 1 2 kd 2 mg(h - d) - 1 2 kd 2 mg(h - d) + 1 2 kd 2 mg(h + d) + 1 2 kd 2 A body of mass 1 kg begins to move under the action of a time dependent force F = (2t , i + 3t 2 , j) N , where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t ? (2t 2 + 3t 3) W (2t 2 + 4t 4) W (2t 3 + 3t 4) W (2t 3 + 3t 5) W A body starts moving unidirectionally under the influence of a source of constant power. Which one of the graph correctly shows the variation of displacement(s) with time (t) ? A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is: 100 m/s 80 m/s 120 m/s 40 m/s A ball is thrown vertically downwards from a height of 20 m with an initial velocity v 0 . It collides with the ground, loses 50 % of its energy in collision and rebounds to the same height. The initial velocity v 0 is: (Take g = 10 m/s 2 ) 20 m/s 10 m/s 14 m/s 25 m/s If a force F = 10 + 0.5x is acting on a particle of mass 2 kg, the change in kinetic energy from x = 0 to x = 2 m is: 21 J 11 J 20 J 22 J Calculate the work done in pulling a body of mass 5 kg up a rough inclined plane of inclination 30 and length 10 m. (Take g = 10 m/s 2 , = 0.2 ) 336.6 J 250 J 500 J 423.2 J Two masses M 1 and M 2 are connected by a spring of spring constant k and are placed on a smooth horizontal surface. A force F pushes M 1 . The maximum compression of the spring is: F M 2 k(M 1+M 2) F M 2 k(M 1+M 2) F M 1 k(M 1+M 2) F k A force F = -k/x (where k is a constant) acts on a particle. The work done by the force in moving the particle from x = 1 to x = e (base of natural log) is: -k k k/e -k/e A bullet of mass 20 g is fired into a wooden block and penetrates 10 cm before coming to rest. If the average resistance is 400 N, the initial velocity of the bullet was: 63.2 m/s 40 m/s 20 m/s 80 m/s A uniform chain of length 2 m and mass 2 kg is lying on a table. If 60 cm of it is hanging over the edge of the table, the work done in pulling the hanging part back onto the table is: ( g = 10 m/s 2 ) 1.8 J 3.6 J 0.6 J 1.2 J A body of mass 2 kg is moved from a point (0,0,0) to (1,1,1) m under the force F = (x i + y j + z k ) N. The work done by the force is: 1.5 J 3 J 1 J 2 J A bullet of mass m hits a target and its velocity is reduced to half after penetrating a distance d . How much further will it penetrate before coming to rest (assuming constant resistance)? d/3 d/4 d/2 d A bullet loses 1/n of its velocity in passing through a single plank. The minimum number of such planks required to stop the bullet completely (assuming constant resistance) is: n 2 2n-1 n 2n-1 n 2 n-1 n n-1 A particle of mass m is moving in a horizontal circle of radius r such that its kinetic energy K varies with the distance traveled s as K = as 2 , where a is a constant. The magnitude of the net force acting on the particle is: 2as 1 + (s/r) 2 2as 2as 2 r as 1 + (r/s) 2 A block of mass m is attached to a vertical spring and lowered slowly until it is in equilibrium. If the spring constant is k , the work done by the external agent in this process is: -m 2g 2/2k m 2g 2/2k m 2g 2/k -m 2g 2/k A force F = (2+x) i acts on a particle. The work done by this force during a displacement from x = 1 to x = 2 is: 3.5 J 2.5 J 4.5 J 5.5 J A particle of mass M moves along a horizontal x axis from x=0 to x=L . The coefficient of kinetic friction varies as a function of x as k(x)= 0- x , where 0, are constants of appropriate dimensions, so that k(L)=0 . The total work done by the frictional force during the motion is n 0MgL , where g is the acceleration due to gravity. The value of n is: 3 1 1 3 1 2 A force F acting on an object varies with distance x as F = kx 1/3 . The work done by the force in moving the object from x = 0 to x = 8 m is: 12k 16k 8k 24k A force F = (3 i + j ) N acts on a particle and displaces it from position r 1 = (2 i + k ) m to r 2 = (4 i + 3 j - k ) m. The work done by the force is: 9 J 6 J 12 J 15 J A body of mass m is moving in a circle of radius r with a constant speed v . The work done by the centripetal force in moving the body over half the circumference of the circle is: Zero mv 2 r r mv 2 r 2r mv 2 A body of mass 2 kg is thrown vertically upwards with a velocity of 20 m/s . Its kinetic energy after 1 second is: ( g = 10 m/s 2 ) 100 J 200 J 400 J 50 J A bullet of mass m is fired with velocity v into a fixed wooden block and comes to rest after penetrating a distance d . If the same bullet is fired into a similar block with velocity 2v , the depth of penetration will be: 4d 2d 2 d 8d A uniform force of 4 N acts on a body of mass 2 kg for 4 s. The change in kinetic energy of the body is: 64 J 32 J 128 J 16 J A spring of force constant k is compressed by x . The work done by the spring force on the agent compressing it is: - 1 2 kx 2 1 2 kx 2 kx 2 -kx 2 Two bodies A and B have masses 1 kg and 4 kg respectively. They are dropped from the same height. The ratio of their momenta after falling for 2 s is: 1:4 1:2 1:1 4:1 A force F = (2 i + 3 j + k ) N is applied to a particle which moves it from position r 1 = (1 i + j + 0 k ) m to r 2 = (2 i + 4 j + 5 k ) m. The work done is: 16 J 10 J 22 J 5 J If the momentum of a body is increased by 20 % , what is the percentage increase in its kinetic energy? 44 % 20 % 40 % 66 % A force F = (20 + 10y) N acts on a particle in y -direction where y is in meters. Work done by this force to move the particle from y = 0 to y = 1 m is: 25 J 30 J 20 J 5 J A force F acting on an object varies with distance x as F = kx 3 . The work done in moving the object from x=1 m to x=2 m is: 15 4 k 7 4 k 15 2 k k 4 If the kinetic energy of a particle is tripled, by what factor does its momentum increase? 3 3 9 1/3 A force F is related to position x as F = x - x 2 . The work done in moving a particle from x = 0 to x = 1 is: 1/6 1/2 1/3 1/4 The work done by a variable force F = 3x 2 in moving a particle from x=1 to x=3 is: 26 units 27 units 28 units 25 units A particle moves under the influence of a force F = kx from x=0 to x=x 1 . The work done is: 1 2 kx 1 2 kx 1 2 kx 1 0 A particle moves from a point (-2 i + 5 j ) to (4 j + 3 k ) when a force of (4 i + 3 j ) N is applied. How much work has been done by the force? 5 J 2 J 8 J 11 J A force F = (2 i + 3 j ) N acting on a particle of mass 2 kg produces a displacement r = (3 i + 4 j ) m. The kinetic energy gained by the particle is: 18 J 24 J 10 J 14 J A force F is related to the position x of a particle as F = (2 + x) N. The work done by this force in moving the particle from x = 1 m to x = 2 m is: 3.5 J 2.5 J 4.5 J 5.5 J If the kinetic energy of a body becomes four times its initial value, then the new momentum will be: Twice the initial momentum Four times the initial momentum Same as the initial momentum Half of the initial momentum The graph between kinetic energy ( K ) and velocity ( v ) of a particle is: A parabola A straight line passing through origin A rectangular hyperbola A circle A force of 10 N displaces an object through 10 m. If the work done is 50 J, then the angle between the force and displacement is: 60 30 45 90 A force F = 2 i + 3 j + k N acts on a body and the body is restricted to move along the z-axis. The work done by the force in moving the body a distance of 2 m along the z-axis is: 2 J 4 J 6 J 1 J An object of mass 500 g is thrown vertically upwards with a speed of 20 m/s. What is the work done by the force of gravity during the time the object reaches its maximum height? -100 J 100 J -50 J 50 J If the momentum of a body is doubled, its kinetic energy becomes: Four times Two times Half Eight times Two particles of mass m 1 and m 2 have equal kinetic energies. The ratio of their velocities v 1 / v 2 is: m 2 / m 1 m 1 / m 2 m 2 / m 1 m 1 / m 2 Which of the following does NOT represent the unit of energy? Watt Electron-volt Kilowatt-hour Joule A block is being pulled on a rough horizontal surface by a force F at an angle with the horizontal. The work done by the normal reaction force is: Zero mg d F d (mg - F ) d A particle moves from rest with a constant power P . The ratio of the velocity of the particle at time t 1 and t 2 is: t 1/t 2 t 1/t 2 (t 1/t 2) 3/2 (t 1/t 2) 1/3 A particle of mass m is moving in a horizontal circle of radius r with a constant speed v . The work done by the centripetal force during one-fourth of a revolution is: Zero m v 2 2 m v 2 4 m v 2 A man of mass 80 kg carries a body of 20 kg on his head and moves a distance of 10 m in the horizontal direction. The work done by the man against gravity is: Zero 1000 J 10000 J 800 J Two masses 1 kg and 4 kg are moving with equal momentum. The ratio of their kinetic energies is: 4 : 1 1 : 4 2 : 1 1 : 2 A spring S 1 and S 2 have spring constants k 1 and k 2 ( k 1 = 2k 2 ). They are stretched by the same distance. The ratio of work done W 1/W 2 is: 2 : 1 1 : 2 4 : 1 1 : 1 If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor: 1/ 2 2 1/2 2 A force F = (5 i + 3 j ) N is applied over a particle which displaces it from origin to the point r = (2 i - 1 j ) m. The work done on the particle is: 7 J 13 J 10 J 11 J Two bodies of mass m 1 and m 2 have equal kinetic energies. If p 1 and p 2 are their respective momenta, then p 1/p 2 is equal to: m 1/m 2 m 1/m 2 (m 1/m 2) 2 1 A particle of mass m is moving in a circular path of radius r with a constant speed v . The work done by the centripetal force during a displacement of 1 4 of the circumference is: Zero mv 2 r mv 2 2 mv 2 If the kinetic energy of a body is increased by 100 % , the percentage increase in its momentum is: 41.4 % 50 % 100 % 200 % A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from x=0 to x=6 m is 18.0 J 13.5 J 4.5 J 9.0 J An object is moving such that its velocity is v = at , where a is a constant. The work done by the resultant force on the object from t=0 to t=T is: 1 2 ma 2T 2 ma 2T 2 1 2 maT 2 1 4 ma 2T 2 An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate which kinetic energy is imparted to water ? 1 2 m 2v 2 1 2 mv 3 mv 3 1 2 mv 2 A uniform force of (3 i + j ) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position (2 i + k ) metre to position (4 i +3 j - k ) metre. The work done by the force on the particle is 9 J 6 J 13 J 15 J A force F=20+10 y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y=0 to y=1 m is 20 J 30 J 5 J 25 J Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10 m/s 2 ) 8.1 kW 12.3 kW 7.0 kW 10.2 kW An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms -1 . The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : ( g = 10 m s -2 ) 20000 34500 23500 23000 The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is 36 10 4 J 36 10 5 J 1 10 5 J 36 10 7 J At any instant of time t , the displacement of any particle is given by 2t - 1 (SI unit) under the influence of force of 5 N . The value of instantaneous power is (in SI unit): 10 5 7 6 The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m . If F A and F B are the forces applied by the breaks on cars A and B respectively, then the ratio of F A F B is 1 2 3 2 2 3 1 3 The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: ( g = 9.8 m/s 2 ) 19.6 kW 19.6 W 39.2 kW 39.2 W If the kinetic energy of a body is increased by 300 % , then the percentage increase in the momentum of the body will be: 100% 200% 50% 400% A force F = -kx acts on a particle. The work done by the force in moving the particle from x = A to x = -A is: Zero -kA 2 1 2 kA 2 - 1 2 kA 2 A force F acting on an object varies with distance x as shown in the figure. The work done by the force in moving the object from x=0 to x=6 m is: 13.5 J 18 J 9 J 4.5 J A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d . The net work done in the process is: mg(h+d) - 1 2 kd 2 mg(h-d) - 1 2 kd 2 mg(h+d) + 1 2 kd 2 mgd + 1 2 kd 2 A body of mass 3 kg is under a constant force which causes a displacement s in meters in time t , given by the relation s = 1 3 t 2 . Work done by the force in 2 seconds is: 8/3 J 19/5 J 5/2 J 3/8 J A block of mass 10 kg , moving in x-direction with a constant speed of 10 m/s , is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m . Its final kinetic energy will be: 475 J 450 J 500 J 250 J A bullet of mass 10 g leaves a rifle at an initial velocity of 1000 m/s and strikes the earth at the same level with a velocity of 500 m/s . The work done in overcoming the resistance of air is: 3750 J 5000 J 2500 J 4750 J A body of mass 4 kg is moving with a momentum of 8 kg m/s . A force of 0.2 N acts on it in the direction of motion for 10 s . The increase in its kinetic energy is: 4.5 J 10 J 8.5 J 2 J A bullet of mass m fired at 30 to the horizontal leaves the barrel of the gun with a velocity v . The bullet hits a soft target at a height h above the ground while it is moving downward and comes to rest inside the target. The total work done on the bullet is: - 1 2 mv 2 1 2 mv 2 + mgh 1 2 mv 2 - mgh -( 1 2 mv 2 + mgh) A uniform force of (2 i + 3 j ) N acts on a particle of mass 1 kg . The work done by the force in 2 s starting from rest is: 13 J 26 J 10 J 20 J A 10 kg body is moved from rest along a horizontal surface by a force of 20 N . If the coefficient of friction is 0.1 , the work done by the net force in 10 s is: ( g = 10 m/s 2 ) 500 J 1000 J 2000 J 250 J A body of mass 5 kg is raised vertically through a distance of 10 m by a force of 100 N . The velocity of the body at the end of 10 m is: ( g = 10 m/s 2 ) 10 2 m/s 10 m/s 20 m/s 5 m/s Two springs A and B have spring constants k A and k B such that k A = 2k B . If they are stretched by the same force F , the ratio of the work done W A / W B is: 1 : 2 2 : 1 1 : 4 4 : 1 A position-dependent force F = 3x 2 - 2x + 7 acts on a body of mass 2 kg and displaces it from x=0 to x=5 m. The work done is: 135 J 125 J 250 J 35 J A body of mass 2 kg is moving under the influence of a force which delivers a constant power of 0.5 W. If the body starts from rest, the speed after 4 s is: 2 m/s 1 m/s 2 m/s 0.5 m/s Which of the following graphs correctly represents the variation of kinetic energy ( K ) of a body with its momentum ( p )? A parabola opening towards the K-axis A straight line through the origin A hyperbola A circle A force F acting on a particle varies with displacement x as F = k/x . The work done from x=x 1 to x=x 2 is: k (x 2/x 1) k(x 2 - x 1) k(1/x 1 - 1/x 2) k(x 2 2 - x 1 2) A body of mass 3 kg is under a force, which causes a displacement in it given by s = 1 3 t 3 (in meters). Find the work done by the force in the first 2 seconds . 24 J 12 J 6 J 18 J A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d . The net work done in the process is: mg(h+d) - 1 2 kd 2 mg(h+d) + 1 2 kd 2 mgh - 1 2 kd 2 mgh + 1 2 kd 2 An engine pumps water continuously through a hose with a velocity v . If m is the mass per unit length of the water jet, what is the rate at which kinetic energy is imparted to water? 1 2 mv 3 1 2 mv 2 mv 3 1 2 m 2v 2 A body of mass m is projected with velocity v at an angle with the horizontal. The work done by gravity from the point of projection to the highest point is: - 1 2 mv 2 2 1 2 mv 2 2 mgv Zero A spring is stretched by 5 cm by a force of 10 N . The work done in stretching it by another 5 cm is: 0.75 J 0.25 J 0.50 J 1.00 J An elevator is moving upward with a constant speed v . A person of mass m is standing in it. The work done by the normal force on the person in time t is: mgvt -mgvt 0 mgv The energy required to accelerate a car from rest to 10 m/s is E . The energy required to accelerate the same car from 10 m/s to 20 m/s is: 3E E 2E 4E A force F is applied to a body of mass m for time t . If the body was initially at rest, the final kinetic energy is: F 2t 2/2m F 2t/2m Ft 2/2m F 2t 2/m A body of mass m moves from rest in a straight line under a constant power P . The velocity at time t is: 2Pt/m Pt/m 2Pt/m Pt 2/m A force F = (5 + 3x) N acts on a particle in the x-direction, where x is in meters. The work done by this force during a displacement from x = 2 m to x = 4 m is: 28 J 14 J 52 J 40 J A body of mass M is dropped from a height h on a sand floor. If the body penetrates x cm into the sand, the average resistance offered by the sand is: Mg(1 + h x ) Mg(h/x) Mghx Mg(1 - h x ) A body of mass m is moving in a straight line with momentum p . A constant force F acts on it in the direction of motion for a distance d . The final momentum of the body is: p 2 + 2mFd p + 2mFd p + Fd p 2 + 2Fd A block of mass 10 kg is pulled by a constant force of 20 N horizontally. If the coefficient of friction is 0.1, find the work done by the friction in moving the block by 5 m. -50 J 50 J -100 J 100 J A force F acting on an object varies with distance x as shown in the force-displacement graph. The work done by the force in moving the object from x = 0 to x = 20 m is: 150 J 200 J 100 J 250 J A force F = (2 + x) i N acts on a particle. The work done by this force in displacing the particle from x = 1.0 m to x = 2.0 m is: 3.5 J 2.5 J 4.5 J 1.5 J A person of mass 60 kg is carrying a load of 20 kg on his head. He moves a distance of 10 m up an incline of 1 in 5 . The work done by him is ( g = 10 m/s 2 ): 1600 J 800 J 4000 J 0 J A force F = (2t) i N acts on a 2 kg particle which is at rest at t = 0 . The work done by the force in the first 2 seconds is: 4 J 2 J 8 J 16 J A force F = ax + bx 2 acts on a particle in the x-direction. The work done by this force in moving the particle from x=0 to x=L is: aL 2 2 + bL 3 3 aL + bL 2 aL 2 2 + bL 3 2 aL 2 + bL 3 A force F = -k/x 2 acts on a particle. The work done by this force in moving the particle from x = a to x = 2a is: -k/2a k/2a k/a -k/a A car of mass 1000 kg is moving at 18 km/h. It is brought to rest in 5 m by applying brakes. The average retarding force is: 2500 N 5000 N 1250 N 1000 N A force F = (7 - 2x + 3x 2) N acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. The work done in joules is: 135 100 120 150 An object of mass 500 g initially at rest is acted upon by a variable force whose X -component varies with X in the manner shown. The speed of the object at X = 25 m is: 20 m/s 25 m/s 30 m/s 40 m/s A force F = (2x i + 3y 2 j ) N acts on a particle. The work done by this force in moving the particle from (0,0) to (1,1) is: 2 J 5 J 1 J 3 J A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P 0 . The instantaneous velocity of this car is proportional to: t 1/2 t 3/2 t t 2 A stone is tied to a string of length L and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u . The magnitude of the change in velocity as it reaches a position where the string is horizontal (speed v ) is: u 2 + v 2 u - v u 2 - v 2 u + v A force F = (x i + 2y j ) N acts on a particle. The work done by this force in moving the particle from the point (2, 1) to (4, 3) is: 14 J 10 J 12 J 16 J A block of mass m is released from the top of a rough inclined plane of height h . If the velocity of the block at the bottom is v , then the work done by the friction force is: 1 2 mv 2 - mgh mgh - 1 2 mv 2 mgh + 1 2 mv 2 -mgh A bucket of mass M is being pulled up from a well of depth h using a rope. If the mass of the rope is m , the total work done is: (M + m 2 )gh (M + m)gh Mgh 1 2 (M + m)gh