Question

An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest rate of change of rotational momentum about their centre of mass is ,

• A. solid sphere
• B. hollow sphere
• C. solid disk
• D. thin hollow cylinder

Answer 1

The correct option is D thin hollow cylinder

$a=\frac{mgsin\theta -f}{m}\alpha =\frac{fr}{m{k}^2}\alpha =a=>mgsin\theta =f(f+\frac{r^2}{k^2})f=\frac{mgsin\theta r}{(1+\frac{r^2}{k^2})}\alpha =\frac{fr}{m{k}^2}=\frac{mgsin\theta r}{(1+\frac{r^2}{k^2})m{k}^2}=\frac{gsin\theta r}{k^2+r^2}$

$\therefore \alpha \propto \frac{1}{k^2}$

$\alpha$ is highest for cylindrical shell.

$\therefore$ rate of change of momentum is highest for cylindrical shell.