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During inelastic collision between two objects, which of the following quantity always remains conserved?

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Important Questions on Work, Energy and Power

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A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles 30° and 60° from vertical (lowest position) are T1 and T2 respectively then
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If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be,
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A mass m is attached to the end of a rod of length l. The mass goes along a vertical circular path with the other end hinged at its centre. What should be the minimum velocity of the mass at the bottom of the circle so that the mass completes the circle?
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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 (g being acceleration due to gravity) is :-
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A body starts from rest with uniform acceleration and acquires a velocity V in time T. The instantaneous kinetic energy of the body after any time t is proportional to:
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Two balls of the same mass are dropped from the same height onto the floor. The first ball bounces upwards from the floor elastically. The second ball sticks to the floor. The first applies an impulse to the floor of I1, the second applies an impulse I2 (for the duration of collision). Then the relation between both the impulses is,
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For a particle moving in a vertical circle,
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A force, F=-kyi^+xj^ where, k is a positive constant, acts on a particle 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 parallel to the y-axis to the point a,a. The total work done by the force F on the particle is,