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  4. 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 .

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Q. 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 $\alpha_{1}$ and $\alpha_{2}$ are the angular accelerations of the cylinder and the sphere respectively, then the ratio $\frac{\alpha_{2}}{\alpha_{1}}$ will be _______.

System of Particles and Rotational Motion

Solution:

$I _{2} \alpha_{2}= I _{1} \alpha_{1}$
$ \frac{2}{5} MR ^{2} \alpha_{2}=\frac{ MR ^{2}}{2} \alpha_{1} $
$\therefore \frac{\alpha_{2}}{\alpha_{1}}=\frac{5}{4}=1.25$