Question

A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be :-

• A. $15:14$
• B. $9:10$
• C. $2:3$
• D. $3:5$

Answer 1

The correct option is A $15:14$

The formula for $ac{c}^n$ of an object $i.e,$ sphere cylender etc$.)$ of mass $,$ radius and $MOI$ given respectively is given by

$a=\frac{g\sin \theta }{1+\frac{I}{M{R}^2}}$

$I$ of spherical shell$,$ $I_{shell}=\frac{2M{R}^2}{3}$

$I$ of solid cylinder$,$ $I_{cyl}=\frac{M{R}^2}{2}$

Therefore$,$ $a_{shell}=\frac{g\sin \theta }{1+\frac{2M{R}^2}{3M{R}^2}}=\frac{g\sin \theta }{\frac{5}{3}}$

$a_{cylinder}=\frac{g\sin \theta }{1+\frac{M{R}^2}{2M{R}^2}}$

Therefore$,=$ $\frac{3}{5}\times \frac{3}{2}=\frac{9}{10}=9:10$

hence$,$

option (B) is correct