Gravitation Question 328

Question: The ratio of radii of earth to another planet is 21 3 and the ratio of their mean densities is 4/5. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is

Options:

A) 1 m

B)0.8 m

C) 0.5 m

D)125 m

Show Answer

Answer:

Correct Answer: B

Solution:

  • to K.E. of the person = P.E. at the maximum height $ [\frac{1}{2}mv^{2}=m\frac{GM}{R^{2}}h.] $ $ [\therefore m\frac{GM}{R^{2}}.h=mG\frac{M’}{R{{’}^{2}}}h’] $

Given $ [\rho =\frac{4}{5}p’,\frac{R}{R’}=\frac{2}{3}] $

$ [\therefore mG.\frac{4}{3}\frac{\pi R^{3}\rho }{R^{2}}.h=mG.\frac{4}{3}\frac{\pi R{{’}^{3}}\rho ‘}{R{{’}^{2}}}.h’] $

$ [\Rightarrow \frac{2}{3}R.\frac{4}{5}\rho ‘1.5=R’\rho ‘h’\therefore h’=0.8m.] $



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