Question

In the figure shown, a ball without sliding on a horizontal surface. It ascends a curved track up to a height $h$ and 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

• A. $h_1=h_2$
• B. $h_1<h_2$
• C. $h_1>h_2$
• D. $h_1=2h_2$

Answer 1

The correct option is C $h_1>h_2$

Case 1: Rough surface with no sliding

The ball will do translational as well as rotational motion (due to the friction)

Work-energy theorem, $mg{h}_1=\frac{1}{2}m{v}^2+\frac{1}{2}I{w}^2$

Case 2: Smooth surface, the ball will do translational motion only.

Work-energy theorem, $mg{h}_2=\frac{1}{2}m{v}^2$

$⟹h_1>h_2$