Question

The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$ from rest, without sliding is

• A. $\sqrt{gh}$
• B. $\sqrt{\left(6/5\right)gh}$
• C. $\sqrt{\left(4/3\right)gh}$
• D. $\sqrt{\left(10/7\right)gh}$

Answer 1

The correct option is D $\sqrt{\left(10/7\right)gh}$

For a solid sphere rolling down from height $h$,

$v=\sqrt{\frac{2gh}{1+\frac{I}{M{R}^2}}}$
and for sphere $I=\frac{2}{5}M{R}^2$
$\therefore v=\sqrt{\frac{2gh}{1+\frac{2}{5}}}=\sqrt{\frac{10}{7}gh}$
Hence, the correct answer is option (d).