A man can jump vertically to a height of 1.5m on the earth. Calculate the radius of a planet of the same mean density as that of the earth from whose gravitational field he could escape by jumping. Radius of earth is 6.41×106m.
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Updated on : 2022-09-05
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h=2geu2 ∴u=2geh (i) For the asked planet this u sbould be equal to the escape velocity from its surface. 2geh=2gpRp or geh=gpRp Re2GMe.h=Rp2GMpRp or Re2(34πRe3)ρh=Rp2(34πRp3)ρRp or Rp=Reh =(6.41×106)(1.5) =3.1×103 m