Question

A metal disc of radius $R$ and mass $M$ freely rolls down from the top of an inclined plane of height $h$ without slipping. The speed of its centre of mass on reaching the bottom of the inclined plane is:

• A. $\sqrt{\frac{4gh}{3}}$
• B. $\sqrt{\frac{3gh}{4}}$
• C. $\sqrt{gh}$
• D. $\sqrt{\frac{gh}{2}}$

Answer 1

The correct option is A $\sqrt{\frac{4gh}{3}}$

Energy should be conserved
Potential energy = Rotational K.E + Translational K.E

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

$mgh=\frac{1}{4}m{r}^2{w}^2+\frac{1}{2}m{v}^2$

$v_{cm}=rw$

$gh=\frac{3}{4}{v}^2$

$v=\sqrt{\frac{4}{3}gh}$