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

Q7.11     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.

Answers (1)

best_answer

The moment of inertia of hollow cylinder is given by   =\ mr^2

And the moment of inertia of solid cylinder is given by :

                                                                                         =\ \frac{2}{5}mr^2

We know that :                \tau \ =\ I\alpha

Let the torque for hollow cylinder be \tau_1 and for solid cylinder let it be \tau_2.

According to the question :                 \tau_1\ =\ \tau_2

So we can write the ratio of the angular acceleration of both the objects.

                                                     \frac{\alpha _2}{\alpha _1}\ =\ \frac{I_1}{I_2}\ =\ \frac{mr^2}{\frac{2}{5}mr^2}\ =\ \frac{2}{5}

Now for angular velocity, 

                                                    \omega \ =\ \omega _o\ +\ \alpha t

Clearly, the angular velocity of the solid sphere is more than the angular velocity of the hollow sphere. (As the angular acceleration of solid sphere is greater).                                                                                

 

Posted by

Devendra Khairwa

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