Question

Three bodies , a ring , a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

• A. The ring body
• B. The solid sphere body
• C. The solid cylinder body
• D. Can't find out

Answer 1

The correct option is B The solid sphere body

Initial total kinetic of the body is zero as the body starts from rest.

As there is no slipping, thus $v=rw$

Let the height by which the body rolls down the surface be $h$.

Using work-energy theorem : $W=K.E_f-K.E_i$

$\therefore$ $mgh=\frac{1}{2}m{v}^2+\frac{1}{2}I{w}^2$

OR $mgh=\frac{1}{2}m{v}^2+\frac{1}{2}km{v}^2$ $(\because I=km{r}^2$ & $v=rw)$

OR $mgh=\frac{1}{2}(1+k)m{v}^2$ $⟹v=\sqrt{\frac{2gh}{1+k}}$

But $k$ is minimum for solid sphere, thus $v$ is maximum for solid sphere.

Hence, solid sphere reaches the ground with maximum velocity.