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Manipal Medical Manipal Medical Solved Paper-2006

  • question_answer
    The length of seconds pendulum is 1 m on earth. If mass and diameter of a planet is doubled than that of earth, then its length becomes:

    A)  1 m              

    B)  2m

    C)  0.5 m            

    D)  4 m

    Correct Answer: C

    Solution :

     \[T=2\pi \sqrt{\frac{l}{g}}\] \[\Rightarrow \] \[2=2\pi \sqrt{\frac{{{R}^{2}}l}{GM}}\]               ...(i) (Here,\[l=1m\]) and on given planet, \[2=2\pi \sqrt{\frac{R{{}^{2}}l}{GM}}\] \[\Rightarrow \] \[2=2\pi \sqrt{\frac{4{{R}^{2}}l}{G\times 2M}}\] ?(ii) From Eqs. (i) and (ii), \[2l=l\] \[\Rightarrow \] \[l~=1/2=0.5m\]


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