Question

A sphere rolls down an inclined plane through a height h. Its velocity at the bottom would be:

• A. $\sqrt{2gh}$
• B. $\sqrt{\frac{7}{10}gh}$
• C. $\sqrt{\frac{10}{7}gh}$
• D. $\left(\sqrt{\frac{10}{7}}\right)gh$

Answer 1

The correct option is A $\sqrt{2gh}$

For a rolling body, the lowest point is the center of rotation.

Thus, velocity of point :

$V_0=V_{em}$

From conservation of Energy

$\frac{1}{2}m{V}_{cm}^2=mgh$

$\Rightarrow V_{cm}=\sqrt{2gh}$ so, $V_o=\sqrt{2gh}$.