In the figure shown, a ball without sliding on a horizontal, surface. It ascends a curved track up to height `h` returns. The value of h is `h_(1)` for sufficiently rough curved track to avoid sliding and is `h_(2)` for smooth curved track then

Options

A. `h_(1)=h_(2)`
B. `h_(1)lth_(2)`
C. `h_(1)gth_(2)`
D. `h_(2)=2h_(1)`

Answer

C

Explanation

If the track is smooth (case `A`) only translational kintetic 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 `h_(1)lth_(2)`