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A man goes at the top of a smooth inclined plane. He releases a bag to fall freely and himself slides down on inclined plane to reach the bottom. If $u_{1}$ and $u_{2}$ are the respective velocities of the man and bag at the bottom of inclined plane, then

(a) $u_{1}>u_{2}$

(b) $u_{1}<u_{2}$

(c) $u_{1}=u_{2}$

(d) $u_{1}$ and $u_{2}$ cannot be compared

The correct option of this question will be (C).

Solution —

The gravitational force is a conservative force, so the work done by it is independent of path. Hence in both cases

$\frac{1}{2} m u^{2}=m g h$

where $h$ is the height of the inclined plane. or $u=\sqrt{2 g h}$

Clearly, it is independent of mass.

$\mathrm{So}, u_{1}=u_{2}$

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