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

Options

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

Answer

B

Explanation

Acceleration of a purely rolling object on an inclined plane is:
`a=(g sin theta)/((1+(K^(2))/(R^(2))))`
for sphereical shell `(K^(2))/(R^(2))=2/3`
for solid cylinder `=(K^(2))/(R^(2))=1/2`
so `(a_("shell"))/(a_("cylinder"))=((g sin theta)/((1+2/3)))/((g sin theta)/((1+1/2)))=9/10`