AIIMS AIIMS Solved Paper-2003

  • question_answer
    An earthquake generates both transverse (S) and longitudinal (P) sound waves in the earth. The speed of S waves is about 4.5 km/s and that of P waves is about 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P wave arrives 4.0 min before the first S wave. The epicentre of the earthquake is located at a distance of about:

    A)  25km   

    B)                        250km 

    C)        2500km              

    D)        5000km

    Correct Answer: C

    Solution :

    Key Idea: Distance travelled by both the waves is same. Let the time taken by the S and P waves to reach the seismograph be \[y\] and \[x\] then \[{{i}_{1}},\] Since, 60s = 1 min \[{{h}^{1/2}}\]   \[h\] Let distance of epicentre be s, then \[{{h}^{3/2}}\] \[{{h}^{2}}\]   \[\beta \] \[[{{M}^{-1}}L{{T}^{-2}}A]\]  \[[{{M}^{-2}}L{{T}^{-2}}{{A}^{-1}}]\] \[[ML{{T}^{-2}}{{A}^{-2}}]\]  \[[ML{{T}^{-1}}{{A}^{-1}}]\] \[{{\beta }^{-}}\]  \[+\frac{G{{M}_{e}}m}{R}=\frac{1}{2}mv_{e}^{2}\] \[{{M}_{e}}\]  \[\therefore \] \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}}\]   \[P+\frac{1}{2}\rho {{v}^{2}}+\rho gh=constant\]


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