Question

A uniform ring of radius R is moving on a horizontal surface with speed v and then climbs up a ramp of inclination ${30}^o$ to a height h. There is no slipping in the entire motion. Then h is?

• A. $v^2/2g$
• B. $v^2/g$
• C. $3v^2/2g$
• D. $2v^2/g$

Answer 1

The correct option is B $v^2/g$

As there is no slipping, energy will be conserved

$\therefore$ initIal K.E= Final P.E

$\therefore \frac{1}{2}{I\omega }^2+\frac{1}{2}m{v}^2=mgh\Rightarrow \frac{1}{2}{m{R}^2\omega }^2+\frac{1}{2}m{v}^2=mgh\frac{1}{2}{mv}^2+\frac{1}{2}m{v}^2=mgh\Rightarrow h=\frac{v^2}{g}$