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.] $
