Four point masses, each of mass m, are fixed at the corners of a… | JEE Main 2020 (6 Sep, Shift 1)

Q42JEE Main 2020 · 6 SEP · SHIFT 1Medium

Rotational Kinetic Energy, Work & Power

Four point masses, each of mass m, are fixed at the corners of a square of side $l$ . The square is rotating with angular frequency $\omega$ , about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is:

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Answer: (a)

Corner on the axis: distance $0$ .
The two corners on the parallel diagonal are at distance $\frac{l}{\sqrt{2}}$ (half the other diagonal).
The opposite corner is at distance $l\sqrt{2}$ (full diagonal).
$I = 2m\frac{l^2}{2} + m(2l^2) = 3ml^2$
$L = I\omega = 3ml^2\omega$
So the answer is (a) $3ml^2\omega$ .

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