Torque of equal magnitude is applied to a solid 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 α1 and α2 are the angular accelerations of the cylinder and the sphere respectively, then the ratio (α2/α1) will be .

Question

Torque of equal magnitude is applied to a solid 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 α1 and α2 are the angular accelerations of the cylinder and the sphere respectively, then the ratio (α2/α1) will be . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

I 2 α2= I 1 α1 (2/5) MR 2 α2=( MR 2/2) α1 ∴ (α2/α1)=(5/4)=1.25

I2​α2​=I1​α1​ 52​MR2α2​=2MR2​α1​ ∴α1​α2​​=45​=1.25

$I_{2} α_{2} = I_{1} α_{1}$
$\frac{2}{5} M R^{2} α_{2} = \frac{M R ^{2}}{2} α_{1}$
$∴ \frac{α _{2}}{α _{1}} = \frac{5}{4} = 1.25$