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JEE Main 2021 (27 Jul, Shift 2) · Rotational Kinetic Energy, Work & Power

Rotational Kinetic Energy, Work & Power question from JEE Main 2021 (27 Jul, Shift 2)

Q40JEE Main 2021 · 27 JUL · SHIFT 2Medium

Rotational Kinetic Energy, Work & Power

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $\left(\frac{I_1}{I_2}\right)$ will be x: 1. The value of x will be _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 9

Belt does not slip, so rim speeds are equal: $\omega_P(3R) = \omega_Q R \Rightarrow \omega_Q = 3\omega_P$
Same KE: $\frac{1}{2}I_1\omega_P^2 = \frac{1}{2}I_2\omega_Q^2$
$\frac{I_1}{I_2} = \left(\frac{\omega_Q}{\omega_P}\right)^2 = 9$
So $x = 9$ .

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