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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2002

  • question_answer
    Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreased by 2% keeping all other quantities same, then

    A)  g decreases by 2% and K decreases by 4%

    B)  g decreases by 4% and K increases by 2%

    C)  g increases by 4% and K increases by 4%

    D)  g decreases by 4% and K increases by 4%

    Correct Answer: C

    Solution :

     \[g=\frac{GM}{{{R}^{2}}}\Rightarrow \frac{\Delta g}{g}=-2\frac{\Delta R}{R}=-2(-2%)=+4%\] And \[K=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}{{\omega }^{2}}\times \frac{2}{5}M{{R}^{2}}\] \[\frac{\Delta K}{K}=2\frac{\Delta R}{R}=2\times (-2)%=-4%\]


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