A solid sphere and a disc. Of same diameter and mass roll down from rest on a frictionless inclined plane. The ratio of their acceleration is :

Options

A. `15:14`
B. `7:8`
C. `1:1`
D. `2:1`

Answer

A

Explanation

`a=(gsintheta)/(1+(I)/(mr^(2)))` for sphere `I=(2)/(5)mr^(2) therefore a_(s)=(5)/(7)gsintheta`
for disc `I=(1)/(2)mr^(2) therefore a_(d)=(2)/(3)gsintheta`
`therefore (a_(s))/(a_(d))=(5)/(7)xx(3)/(2)=(15)/(14)`