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 ?

A solid cylinder and a hollow cylinder , both of the same mass and sam

1.	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 ?
Answer» Both together only when angle of inclination of PLANE is `45^(@)` Both together Hollow cylinder Solid cylinder Solution :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 .