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 α 1 and α 2 are the angular accelerations of the cylinder and the sphere respectively, then the ratio (α 1/α 2) 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 α 1 and α 2 are the angular accelerations of the cylinder and the sphere respectively, then the ratio (α 1/α 2) will be (A) (5/2) (B) (5/4) (C) (4/5) (D) (2/5)

Tardigrade Admin · Accepted Answer

α 1=(M R2/2) and α 2=(2/5)MR2 ∴ (α 1/α 2)=(4/5)

$\frac{5}{2}$

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{2}{5}$

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

25​

45​

54​

52​

α1​=2MR2​ and α2​=52​MR2 ∴α2​α1​​=54​

$\frac{5}{2}$

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{2}{5}$

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