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A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x)=kx+a x 3 . Here k and a are positive constants. For x0 , the functional from of the potential energy U(x) of the particle is

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Important Questions on Work, Energy and Power

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A particle of charge Q and mass m travels through a potential difference V from rest. The final momentum of the particle is:
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An electron moving in a electric potential field V1 enters a higher electric potential field V2,, then the change in kinetic energy of the electron is proportional to:-
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In a crystal the atoms are located at the position of ________.       

 

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A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is:
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A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of the kinetic energy of P to the kinetic energy of S is

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The velocity of centre of mass of a disc rolling on an inclined plane changes from V to 2 V at any instant of time. If M is the mass of disc then increases in its kinetic energy will be
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A uniform thin ring of mass 0.4 kg rolls without slipping on a horizontal surface with a linear velocity of 10 cm/s. The kinetic energy of the ring is :
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The velocity of simple pendulum is maximum at