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WB JEE Medical WB JEE Medical Solved Paper-2011

  • question_answer
    If the earth were to suddenly contract to \[\frac{\text{1}}{\text{n}}\text{th}\] of its present radius without any change in its mass, the duration of the new day will be nearly

    A)  \[24/n\,h\]                       

    B)  \[24n\,h\]

    C)  \[24/{{n}^{2}}\,h\]                        

    D)  \[24\,{{n}^{2}}\,h\]

    Correct Answer: C

    Solution :

                     From the conservation of momentum, we have \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] Thus, we get    \[\frac{2}{5}M{{R}^{2}}\left( \frac{2\pi }{{{T}_{1}}} \right)=\frac{2}{5}M\frac{{{R}^{2}}}{{{n}^{2}}}\left( \frac{2\pi }{{{T}_{2}}} \right)\] Hence, we get \[{{T}_{2}}=\frac{{{T}_{1}}}{{{n}^{2}}}=\frac{24}{{{n}^{2}}}h\]


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