Question

In the figure shown, a ring A is initially rolling without sliding with a velocity v on the horizontal surface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity what will be the maximum height reached by A on B.

• A. $\frac{v^2}{2g}$
• B. $\frac{v^2}{3g}$
• C. $\frac{v^2}{4g}$
• D. $\frac{v^2}{5g}$

Answer 1

The correct option is C

$\frac{v^2}{4g}$

When ring is at maximum height, the wedge and ring have same x component of velocity. In the absence of friction between ring and wedge surface, angular velocity of ring remain constant. $\frac{1}{2}m{v}^2,\frac{1}{2}I{\omega }^2=\frac{1}{2}m{v}_1^2+\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}_1^2+mgh$ where $v_1$ is final common velocity $v_1=\frac{v}{2}=>h=\frac{V^2}{4g}$