A solid cylinder and a hollow cylinder , both of the same mass and same external diameter are released from the same height at the same time on an inclined plane . Both roll down without slipping . Which one will reach the bottom first ?

Options

A. Both together only when angle of inclination of plane is `45^(@)`
B. Both together
C. Hollow cylinder
D. Solid cylinder

Answer

D

Explanation

Time taken to reach the bottom of inclined plane is `t = sqrt((2 I (1 + (K^(2))/(R^(2))))/(g sin theta))`
Here , l is length of incline plane
For solid cylinder `K^(2) = (R^2)/(2)`
For hollow cylinder `K^2 - R^2`
Hence , solid cylinder will reach the bottom first .