Question

The track shown in figure ends in a circular track of radius $r$ with centre at O. A small solid sphere of mass $m$ rolls from rest without slipping from a point A at a height $h=6r$ from the level ground. The speed of the sphere when it reaches a point B at height $r$ above the level ground is :

• A. $\sqrt{10gr}$
• B. $\sqrt{\frac{50}{7}gr}$
• C. $\sqrt{\frac{22}{7}gr}$
• D. $zero$

Answer 1

Answer: (B)

$\sqrt{\frac{50}{7}gr}$

$ByconservationofEnergymg\left(5r\right)=mgr+\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2\Rightarrow mg\left(5r\right)=mgr+\frac{1}{2}m{v}^2+\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\omega }^2\Rightarrow mg\left(5r\right)=mgr+\frac{1}{2}m{v}^2+\frac{1}{2}\left(\frac{2}{5}m\right)v^2\Rightarrow v=\sqrt{\frac{50}{7}gr}$