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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion2 Marks
Question
If earth contracts to half its radius, what would be the duration of the day? Ans. According to the law of conservation of angular momentum,
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Answer

$\text{I}_1\omega_1=\text{I}_2\omega_2$ $\Rightarrow\frac{\text{I}_1}{\text{T}_1}=\frac{\text{I}_2}{\text{T}_2}\text{ or }\text{T}_2=\frac{\text{I}_2}{\text{I}_1}\text{T}_1$ $\text{I}_1=\frac{2}{5}\text{MR}^2,\text{I}_2=\frac{2}{5}\text{M}\Big(\frac{\text{R}}{2}\Big)^2$ $\therefore\text{T}_1=\frac{1}{4}\times24=6\text{hr.}$

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