Three bodies a ring (R ) , a solid cylinder (C ) and a solid sphere (S ) having same mass and same radius roll down the inclined plane without slipping . They start from rest , if `V_(R),V_(C)` ans `V_(S)` are velocities of respective bodies on reaching the bottom of the plane then

Options

A. `v_(R )=v_(C )=v_(S)`
B. `v_(R)gtv_(C)gtv_(S)`
C. `v_(R)ltv_(C)ltv_(S)`
D. `v_(R)=v_(C)gtv_(S)`

Answer

C

Explanation

`mgh=(1)/(2)mv^(2)+(1)/(2)Iomega^(2)`
`mgh=(1)/(2)mv^(2)+(1)/(2)I(v^(2))/(R^(2))=(1)/(2)v^(2)(m+(I)/(R^(2)))`
`v=sqrt((2mgh)/((m+(I)/(R^(2)))))implies` more I, less v
`implies v_(R)ltv_(C)ltv_(S)`