Question

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

• A. $gsin\alpha$
• B. $2/3gsin\alpha$
• C. $1/2gsin\alpha$
• D. $1/3gsin\alpha$

Answer 1

Answer: (B)

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

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