Torques of equal magnitude are applied to a hollow cylinder and a soli

1.	Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and 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.
Answer» M.I of the cylinder = I₁ = MR² and M.I. of the sphere = I₂ = 2/5 MR² Angular acceleration of the cylinder, α₁ = τ/I₁ = {τ}/{MR₂} Angular acceleration of the sphere, α₂ = τ/I₂ = {τ}/{2/5 MR₂} = {2.5 τ}/{MR₂} = 2.5 α₁ It is clear that the sphere will acquire a greater angular acceleration.

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and 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.

Answer»

M.I of the cylinder = I₁ = MR²

and M.I. of the sphere = I₂ = 2/5 MR²

Angular acceleration of the cylinder,

α₁ = τ/I₁ = {τ}/{MR₂}

Angular acceleration of the sphere,

α₂ = τ/I₂ = {τ}/{2/5 MR₂} = {2.5 τ}/{MR₂} = 2.5 α₁

It is clear that the sphere will acquire a greater angular acceleration.