A wheel is rotating freely with an angular speed ω on a shaft. The… | JEE Main 2020 (5 Sep, Shift 1)

Q53JEE Main 2020 · 5 SEP · SHIFT 1Medium

Angular Momentum & its Conservation

A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

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Answer: (d)

$I\omega=(I+3I)\omega'$ , so $\omega'=\frac{\omega}{4}$ .
$K_f=\frac12(4I)\frac{\omega^2}{16}=\frac{I\omega^2}{8}$ , $K_i=\frac{I\omega^2}{2}$
Fractional loss $=1-\frac{1/8}{1/2}=\frac34$
So the answer is (d) $\frac34$ .

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