Question

A disc and a ring of same mass are rolling. If their kinetic energies are equal, then find the ratio of their velocities.

Answer 1

Answer:

Since they have same mass and have equal kinetic energy, therefore their velocity is also equal. So, the ratio will be 1:1.

Explanation:

DERIVE IT MATHEMATICALLY.

Answer 2

$\frac{v_d}{v_r}= \sqrt{2}$  is the ratio of their velocities.

Explanation:

moment of inertia of the disk:

$I=\frac{1}{2} m.R_d^2$

moment of inertia of the ring:

$I=m.R_r^2$

To accommodate the same mass the size of the ring has to be larger hence its radius will be larger than that of disk if made of same material.

Now since their kinetic energies are equal:

$KE_d=KE_r$

$\frac{1}{2} I_d.\omega_d^2=\frac{1}{2} I_r.\omega_r^2$

$\frac{1}{2} m.R_d^2\times (\frac{v_d}{R_d} )^2=m.R_r^2\times (\frac{v_r}{R_r} )^2$

$\frac{v_d^2}{2} =v_r^2$

$\frac{v_d}{v_r}= \sqrt{2}$

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TOPIC: moment of inertia

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