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JEE Main 2024 (6 Apr, Shift 1) · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from JEE Main 2024 (6 Apr, Shift 1)

Q28JEE Main 2024 · 6 APR · SHIFT 1Medium

Angular Momentum & its Conservation

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ________ hours 30 minutes.

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

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Answer: 13

$L=I\omega$ conserved, $I=\frac25MR^2$ , so $T\propto I\propto R^2$ .
$T'=24\times\left(\frac34\right)^2=24\times\frac{9}{16}=13.5$ h
$T'=13$ h 30 min, so the answer is 13.

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