The 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 a inclinded plane. Both roll down without slipping which one will reach the bottom first?

Both together only when angle of inclination of plane is 45^o

Both together

Hollow cylinder

Solid cylinder

Solution

Both together

straight t space equals space fraction numerator 1 over denominator sin space straight theta end fraction square root of fraction numerator 2 straight h over denominator straight g end fraction open parentheses 1 plus straight k squared over straight R squared close parentheses end root If space straight a space solid space and space hollow space body space of space same space shape space are space allowed space to space roll space down space on space inclined space plane space then space as space open parentheses straight k squared over straight R squared close parentheses subscript straight s less than space open parentheses straight k squared over straight R squared close parentheses subscript straight H comma space solid space body space will space reach space the space bottom first space with space greater space velocity.

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