Torques of equal magnitude are applied to hollow cylinder and a solid sphere, both having the same mass and same radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. which of the two will acquire a greater angular speed after a given time ?

Explanation

Let `omega_(1) andomega_(2)` to be the angular velocities of hollow cylinder and solid sphere respectively.
Let m = mass of solid sphere and hollow sphere Moment of inertia of hollow cylinder
`(1)/(2) MR^(2)`
Moment of inertia of solid sphere `=(2)/(5)MR^(2)`
Since torque applied is same, (using `tau=I alpha)`
`I_(1) alpha_(1)=I_(2) alpha_(2)`
`(I_(1))/(I_(2))=(alpha_(2))/(alpha_(1)) or (alpha_(2))/(alpha_(1)) =(I_(1))/(I_(2))=(MR^(2))/((2)/(5)MR^(2))=(5)/(2)`
As `omega=omega_(0)+alpha t` we can say that for a given value of `omega_(0) and t, omega_(2) omgea_(1)`
`rArr` The angular speed of solid sphere is greater than the angular speed of hollow cylinder.