Torques of equal magnitude are applied to a thin hollow cylinder and a solid sphere, both having the same mass and radius. Both of them are free to rotate about their axis of symmetry. If `alpha_(c) and alpha_(s)` are the angular accelerations of the cylinder and the sphere respectively, then the ratio `(alpha_(c))/(alpha_(s))` will be

Options

A. `(5)/(2)`
B. `(2)/(5)`
C. `(4)/(3)`
D. `(3)/(4)`

Answer

B

Explanation

`tau=Ialpha`
Torques of equal magnitude are applied to the hollow cylinder and the solid sphere.
`therefore I_(c)alpha_(c)=I_(s)alpha_(s)`
`therefore" "(alpha_(c))/(alpha_(s))=(I_(s))/(I_(c))=((2)/(5)MR^(2))/(MR^(2))=(2)/(5)`
[Note : A ring is a transverse section of a hollow cylinder. Hence the M.I. of the hollow cylinder = M.I. of the ring = `MR^(2)`.