First slide

Rolling motion

Question

In the figure shown, a ball without sliding on a horizontal surface. It ascends a curved track up to height h and returns. The value of h is h₁ for sufficiently rough curved track to avoid sliding and is h₂ for smooth curved track, then

Moderate

A

$h_{1} = h_{2}$
B

$h_{1} < h_{2}$
C

$h_{1} > h_{2}$
D

$h_{2} = 2 h_{1}$

Solution

If the track is smooth (case A), only translational kinetic energy changes to gravitational potential energy. But, if the track is rough (case B), both translational and
rotational kinetic energies change to potential energy.
Therefore, potential energy (= mgh) will be more in case B than in case A.
Hence, h₁>h₂.

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