When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude , where a and b are constants. The work done in stretching the unstretched rubber band by L is
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A force (where k is a positive constant) acts on a particle is moving in the x-y 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 F on the particle is
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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 acceleration due to gravity , the work required to pull the hanging part on to the table is
1. MgL
2. MgL/3
3. MgL/9
4. MgL/18
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
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An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum exention in the spring is
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A particle, which is constrained to move along 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) = . Here, k and a are positive constants. For x0, the functional form of the potential energy U (x) of the particle is
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A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to
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A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of
1. (2/3) k
2. (3/2) k
3. 3 k
4. 6 k
A particle moves in a straight line with retardation proportional to its displacement. The loss of kinetic energy during a displacement x is proportional to
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The potential energy of a 1 kg particle free to move along the x-axis is given by U(x) =
The total mechanical energy of the particle is 2 J. Then, the maximum speed in (m/s) is
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A uniform chain has a mass M and length L. It is placed on a frictionless table with length hanging over the edge. The chain begins to slide down. Then the speed v with which the end slides away from the edge is given by
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. The work done by the variable force along OA
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