Question

The ratio of the acceleration for a solid sphere ( mass m and radius R) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is

• A. 5:7
• B. 2:3
• C. 2:5
• D. 7;5

Answer 1

The correct option is A 5:7

Note: In general down the incline:-

$a=\frac{g\sin \theta }{1+\frac{k^2}{R^2}}f=\frac{mg\sin \theta }{1+\frac{R^2}{k^2}}$

all of some shaped body $a$ is independent of that size, mass , density etc.

Here $k\to$ Radius of gyration

$R\to$ Radius of the rolling body

without Rolling-

$a_1=g\sin \theta$

during Rolling $a_2=\frac{2}{5}g\sin \theta$

$\frac{a_2}{a_1}=\frac{2}{5}$