Question

A uniform disc of mass 'm' and radius R is rolling down a fixed inclined plane without slipping. The angular acceleration of the disc is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We know that ,

$a_{cm}$ = $\frac{gsing\theta }{1+\frac{K^2}{R^2}}$ = $\frac{1}{2}$

For disc, I = $\frac{M{R}^2}{2}$ = M$K^2$

$\Rightarrow$ $\frac{K^2}{R^2}$ = $\frac{1}{2}$

$\Rightarrow$ $a_{cm}$ = $\frac{gsin\theta }{1+\frac{1}{2}}$ = $\frac{2}{3}$ g sin $\theta$

$\therefore$ Angular acceleration , $\alpha$ = $\frac{a_{c}m}{R}$ [ $\therefore$ For pure rolling , $a_{cm}$ = r $\alpha$ ]

$\Rightarrow$ $\alpha$ = $\frac{2gsin\theta }{3R}$