Question

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

• A. $\sqrt{\frac{10}{7}gh}$
• B. $\sqrt{gh}$
• C. $\sqrt{\frac{6}{5}gh}$
• D. $\sqrt{\frac{4}{3}gh}$

Answer 1

The correct option is A $\sqrt{\frac{10}{7}gh}$

$Mgh=\frac{1}{2}M{v}^2+\frac{1}{2}I{\omega }^2[v=Rw]$

$Mgh=\frac{1}{2}M{v}^2+\frac{1}{2}\times \frac{2}{5}M{R}^2\times \frac{v^2}{R^2}$

$gh=\frac{v^2}{2}+\frac{v^2}{5}=\frac{7}{10}{v}^2$

$⟹v=\sqrt{\frac{10}{7}gh}$