Question

The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle $ \alpha $ is

• A. $ g \, sin \, \alpha $
• B. $ 2/3 \, g \, sin \, \alpha $
• C. $ 1/2 \, g \, sin \, \alpha $
• D. $ 1/3 \, g \, sin \, \alpha $

Answer 1

Answer: (B)

The acceleration of the body which is rolling down an inclined plane of angle $\alpha$ is

$a=\frac{g\,sin\,\alpha}{1+\frac{K^{2}}{R^{2}}}$
where $K=$ radius of gyration,
$R=$ radius of body
Now, here the body is a uniform solid disc
So, $\frac{K^{2}}{R^{2}}=\frac{1}{2}$
$\therefore a=\frac{g\,sin\,\alpha}{1+\frac{1}{2}}$
or $a=\frac{g\,sin\, \alpha}{\frac{3}{2}}$
or $a=\frac{2\,g\,sin\,\alpha}{3}$