When a uniform solid sphere and a disc of the same mass and of the same radius roll down an inclined smooth plane from rest to the same distance, then ratio of the time taken by them is

Options

A. `15:14`
B. `15^(2):14^(2)`
C. `sqrt(14):sqrt(15)`
D. `14:15`

Answer

C

Explanation

`t=(1)/(sin theta)sqrt((2h)/(g)(1+(K^(2))/(R^(2))))`
`(t_(S))/(t_(D))=sqrt((1+((K^(2))/(R^(2)))_(S))/(1+((K^(2))/(R^(2)))_(D)))=sqrt((1+(2)/(5))/(1+(1)/(2)))=sqrt((14)/(15))`