Potential Energy & Conservation — Practice Questions

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

A spring of spring constant k is stretched by a distance x from its natural length. It is then stretched further by a distance 2x . The additional work done in the second stretching is: 4kx 2 1 2 kx 2 2kx 2 9 2 kx 2 Two springs of spring constants k 1 and k 2 ( k 1 > k 2 ) are stretched by the same force. If W 1 and W 2 are the work done in stretching the springs, then: W 1 < W 2 W 1 > W 2 W 1 = W 2 W 1 = W 2 = 0 The work done in stretching a spring of spring constant k from an extension x to 2x is: 3 2 kx 2 1 2 kx 2 kx 2 2kx 2 The potential energy of a particle varies with distance x as U(x) = ax 2 - bx . The force acting on the particle is zero at: x = b/2a x = a/b x = b/a x = 2b/a A spring of force constant k is cut into two equal parts. The force constant of each part is: 2k k/2 k 4k A vertical spring is compressed by a distance x and a ball of mass m is placed on it. When the spring is released, the ball rises to a height h . The spring constant k is: 2mgh/x 2 mgh/x 2 2mgh/x mgh/x The work done by a conservative force along a closed path is: Zero Positive Negative Depends on the path A body of mass 2 kg is moved up a smooth inclined plane of inclination 30 to a height of 5 m. The work done is: ( g = 10 m/s 2 ) 100 J 50 J 200 J 173.2 J A body of mass m is projected with velocity v at an angle of 45 with the horizontal. The work done by gravity during its entire flight is: Zero -mgv 2/g mgv 2/g 1/2 mv 2 A ball is dropped from a height h . As it bounces off the floor, its speed becomes 80 % of its speed just before hitting the floor. The ball will rebound to a height of: 0.64h 0.80h 0.40h 0.50h A block of mass M is suspended from a light spring of force constant k . Another mass m is placed on M . The increase in the equilibrium compression is: mg/k (M+m)g/k Mg/k mg Which of the following statements is true for a conservative force? Work done in a closed path is zero Work done depends on the path taken It can dissipate energy as heat The total mechanical energy is not conserved A spring with spring constant k is compressed by x . The work done by the spring force is: - 1 2 kx 2 1 2 kx 2 kx -kx For a particle in a conservative field, the relation between force F and potential energy U is: F = -dU/dx F = dU/dx U = -dF/dx F = - U dx When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched by a further 2 cm, the stored energy will be: 400 J 200 J 300 J 100 J The potential energy of a system increases if work is done: By the system against a conservative force By the system against a non-conservative force Upon the system by a conservative force Upon the system by a non-conservative force An object of mass 5 kg is released from the top of a smooth inclined plane of height 20 m. Its kinetic energy when it reaches the bottom is: ( g = 10 m/s 2 ) 1000 J 500 J 200 J 2000 J A body of mass 2 kg falls from a height of 10 m and rebounds to a height of 5 m. The loss of energy is: ( g = 10 m/s 2 ) 100 J 50 J 200 J 10 J A body of mass 2 kg is thrown up with a kinetic energy of 490 J . The height at which its kinetic energy becomes half of its original value is: (Take g = 9.8 m/s 2 ) 12.5 m 25 m 10 m 50 m A particle of mass m is moving in a vertical circle of radius r . The minimum velocity required at the lowest point to just reach the horizontal position (level with center) is: 2gr gr 3gr 5gr A block of mass m is connected to a spring of spring constant k . The spring is stretched by a distance x from its equilibrium position. The work done by the spring force is: - 1 2 kx 2 1 2 kx 2 -kx 2 kx 2 An object of mass 1 kg is falling from a height of 10 m. When it reaches 5 m from the ground, its total mechanical energy is ( g = 10 m/s 2 ): 100 J 50 J 150 J 200 J Which of the following is a non-conservative force? Viscous force Electrostatic force Gravitational force Magnetic force A block of mass m is released from rest from a height h on a smooth curved track that ends in a horizontal section. The horizontal section has a spring of constant k fixed to a wall. The maximum compression of the spring is: 2mgh k mgh k 2mgh k mgh 2k The potential energy of a particle is U(x) = k(1 - e -x 2 ) . The force acting on the particle at x=0 is: 0 k 2k k/2 The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is:- 4U 8U 16U U 4 A body of mass 1 kg of thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18m. How much energy is lost due to air friction ? ( g = 10 m/s 2 ) 10 J 20 J 30 J 40 J A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is : [Latent heat of ice is 3.4 10 5 J/kg and g = 10 N/kg] 34 km 544 km 136 km 68 km The potential energy of a long spring when stretched by 2 cm is U . If the spring is stretched by 8 cm, potential energy stored in it will be 2U 4U 8U 16U A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, the work required to pull the hanging part on to the table is: MgL 18 MgL 3 MgL 9 MgL 6 A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant k . The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be: 2Mg/k Mg/k Mg/2k 4Mg/k A bob of a simple pendulum of length L is released from a horizontal position. The tension in the string when the bob passes through the lowest point is: 3mg mg 2mg Zero A block of mass m is pushed against a spring of spring constant k fixed at one end to a wall. The block can slide on a frictionless horizontal surface. The block is released from the compressed state where the spring is compressed by x 0 . The speed of the block when the spring is compressed by x 0/2 is: x 0 2 3k m x 0 2 k m x 0 k m x 0 2 2k m Two masses M and m are connected by a weightless string passed over a frictionless pulley. If M > m , the loss in potential energy of the system when M descends through a distance h is: (M-m)gh (M+m)gh Mgh mgh A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -k/r 2 , where k is a constant. The total energy of the particle is: -k/2r -k/r k/2r k/r The potential energy of a particle in a force field is U = A r 2 - B r , where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is: 2A/B A/B B/2A A/2B A body of mass 1 kg is thrown vertically upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air resistance? (Take g = 10 m/s 2 ) 20 J 30 J 40 J 10 J For a stable equilibrium, the potential energy U of a particle as a function of its position x must satisfy: dU/dx = 0 and d 2U/dx 2 > 0 dU/dx = 0 and d 2U/dx 2 < 0 dU/dx = 0 and d 2U/dx 2 = 0 dU/dx 0 and d 2U/dx 2 > 0 The potential energy of a particle in a certain field is given by U = a r 2 - b r , where a and b are positive constants. The distance of the particle from the center for stable equilibrium is: 2a/b a/b a/2b b/2a A 1 kg block is moving with a velocity of 4 m/s on a smooth horizontal surface. It hits a spring of force constant k = 400 N/m . The maximum compression of the spring is: 0.2 m 0.4 m 0.1 m 0.5 m A ball is thrown vertically up with velocity v . At what height will its kinetic energy be reduced to 25 % of its initial value? 3v 2 8g v 2 8g v 2 4g 3v 2 4g A spring of spring constant k is stretched by a distance x . The work done is W . If it is further stretched by another distance x , the additional work done is: 3W W 2W 4W A block is kept on a frictionless surface. A spring of constant k is compressed by x 0 and then released. The maximum velocity of the block of mass m will be: x 0 k/m kx 0/m x 0 m/k k x 0 / m The potential energy of a particle in a conservative field is U = Ax 2 - Bx . The force acting on the particle is zero at x equal to: B / 2A A / B B / A 2B / A A particle is moving under the influence of a conservative force. Which of the following graphs represents the variation of its total mechanical energy E with its displacement x ? A horizontal straight line A straight line passing through origin A parabola opening upwards A hyperbola A particle of mass m is moving in a vertical circle. The tension in the string at the lowest point is T L and at the highest point is T H . The difference (T L - T H) is: 6mg 3mg 4mg 2mg The potential energy of a particle in a region is given by U = 10x 2 + 5y 2 . The force acting on the particle at (1, 2) is: -20 i - 20 j 20 i + 20 j -10 i - 10 j 10 i + 10 j A body of mass 2 kg is thrown upward with a speed of 10 m/s . The work done by the force of gravity during the first 2 seconds is ( g = 10 m/s 2 ): Zero -200 J 200 J -100 J A spring of force constant k is stretched by x . The work done in stretching it further by x is: 3 2 kx 2 1 2 kx 2 kx 2 2kx 2 A vertical spring is fixed at its lower end. A block of mass m is dropped from a height h onto the free end of the spring. The maximum compression x is given by the equation: 1 2 kx 2 = mg(h+x) 1 2 kx 2 = mgh 1 2 kx 2 = mgx 1 2 kx 2 + mgh = mgx 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 amount of work, the ratio of the forces F A/F B will be: 2 2 1 2 4 The potential energy of a system is given by U = x 2 - 8x . The position of equilibrium and its nature are: x = 4 , Stable x = 4 , Unstable x = 8 , Stable x = 0 , Unstable A uniform rope of mass m and length L is lying on a smooth horizontal floor. The work done in lifting one end of the rope to a height L so that it hangs vertically is: mgL/2 mgL mgL/4 2mgL A point mass m is whirled in a vertical circle of radius R by a string. The ratio of the kinetic energy of the mass at the lowest point to that at the highest point, if it just completes the vertical circle, is: 5 : 1 3 : 1 2 : 1 4 : 1 A solid cube of mass m and side a is lying on a horizontal surface. The minimum work required to tilt the cube about one of its edges so that its diagonal becomes vertical is: mg a 2 ( 2 -1) mg a( 2 -1) mg a 2 mg a 2 A spring with spring constant k is divided into two parts of length ratio 1:2 . The spring constant of the smaller part is: 3k k/3 3k/2 2k The potential energy between two atoms in a molecule is given by U(r) = a r 12 - b r 6 . The atoms are in stable equilibrium when the force between them is: Zero Maximum Minimum b 2/4a A block of mass 2 kg is dropped from a height of 40 cm onto a vertical spring of force constant 1960 N/m. The maximum compression of the spring is: 10 cm 5 cm 20 cm 15 cm The potential energy of a particle of mass m free to move along the x-axis is given by U(x) = kx 2/2 for x > 0 and U(x) = 0 for x < 0 . If the total mechanical energy of the particle is E , then its speed at x = 2E/k is: Zero E/m 2E/m E/2m A point mass m is whirled in a vertical circle of radius R using a string. The difference in kinetic energy of the mass at the lowest and highest point for the string to just remain taut is: 2mgR 2.5mgR 5mgR mgR A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively S 4 , 3gS 2 S 2 , 3gS 2 S 4 , 3gS 2 S 4 , 3gS 2 A potential energy function is given by U(x) = A x 12 - B x 6 , where A and B are positive constants. The distance x at which the particle is in stable equilibrium is: ( 2A B ) 1/6 ( A B ) 1/6 ( B 2A ) 1/6 ( 2B A ) 1/6 A particle of mass m is moving in a vertical circle of radius r . If the velocity of the particle at the highest point is 7gr , then the tension in the string at the lowest point is: 12mg 6mg 9mg 10mg A particle of mass m is moving in a horizontal circle of radius r under a centripetal force given by F = - k r 2 . The total energy of the particle is: - k 2r k 2r - k r k r For a particle moving in a potential U(x) = k 2 (x 2 - x 4) , the points of stable equilibrium are at: x = 0 x = 1 x = 1 2 No stable equilibrium A block of mass m is attached to a vertical spring of spring constant k . If the block is released from rest when the spring is in its natural length, the maximum velocity attained by the block is: g m/k 2g m/k g 2m/k 1 2 g m/k A body of mass m is moving in a vertical circle of radius r . The work done by the force of gravity as the body moves from the lowest point to the highest point is: -2mgr 2mgr mgr Zero For a particle moving in a potential U(x) = ax 2 - bx 4 , the position of stable equilibrium is: x = 0 x = a/2b x = - a/2b No stable equilibrium exists Two blocks of masses m 1 and m 2 are connected by a spring of spring constant k and placed on a smooth horizontal surface. If m 1 is suddenly given a velocity v away from m 2 , the maximum extension in the spring will be: v m 1 m 2 (m 1 + m 2)k v m 1 k v m 2 k v m 1 + m 2 k A mass m is attached to a string of length L and released from a horizontal position. As the string sweeps through the vertical, it strikes a fixed peg at distance d below the point of suspension. For the mass to complete a circle around the peg, the minimum value of d must be: 3L/5 2L/5 L/2 4L/5 A ball is thrown vertically upwards with a velocity u . If the air resistance provides a constant retarding force f , the ratio of the time of ascent to the time of descent is: g-f/m g+f/m g+f/m g-f/m g-f/m g+f/m 1 A uniform metal rod of length L and mass M is held vertically on a smooth floor. When it is released, its lower end does not slip. The velocity of the upper end when it hits the floor is: 3gL 2gL gL 3/2 gL What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R at the lowest point so as to complete the loop? 5gR 2gR 3gR gR A potential energy function is U = k(x+y) . The force acting on the particle is: -k( i + j ) k( i + j ) -k( i - j ) k( i - j )