Q139 / 160 · WBJEE 2011 · Physics

If the Earth were to suddenly contract to \(\frac{1}{n}\) th of its present radius without any change in its mass, the duration of the new day will be nearly

  • A
    \(24 / \mathrm{n} \mathrm{hr}\).
  • B
    \(24 \mathrm{n} \mathrm{hr}\).
  • Correct answer
    C
    \(24 / \mathrm{n}^2 \mathrm{hr}\).
  • D
    \(24 n^2 h r\).

Solution

Hints: \(\mathrm{I}_1 \omega_1=\mathrm{I}_2 \omega_2\) \(\begin{aligned} & \frac{2}{5} \mathrm{MR}^2\left(\frac{2 \pi}{\mathrm{T}_1}\right)=\frac{2}{5} \mathrm{M} \cdot \frac{\mathrm{R}^2}{\mathrm{n}^2}\left(\frac{2 \pi}{\mathrm{T}_2}\right) \\ & \mathrm{T}_2=\frac{\mathrm{T}_1}{\mathrm{n}^2}=\frac{24}{\mathrm{n}^2} \end{aligned}\)

Hence, the correct answer is option: 'C'.

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