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 taking lowest time to reach down the inclined plane is

• A. solid sphere
• B. spherical shell
• C. solid disk
• D. thin cylinder

Answer 1

The correct option is A solid sphere

$a=\frac{(mg\sin \theta -f)}{m}\alpha =\frac{fr}{m{k}^2}r\alpha =aa=\frac{g\sin \theta }{(1+\frac{k^2}{r^2})}\frac{1}{2}a{t}^2=l\sec \theta t\propto {\left(\frac{1}{a}\right)}^{1/2}t\propto {(1+\frac{k^2}{r^2})}^{1/2}$

higher $\frac{k^2}{r^2}$ implies high time, so lowest time is teken by, solid sphere.