A) 2624 km
B) 3000 km
C) 2020 km
D) none of these
Correct Answer: A
Solution :
From Newtons law of gravitation \[F=\frac{G{{M}_{e}}m}{R_{e}^{2}}\] ???.. (i) where G is gravitational constant,\[{{M}_{e}}\]the mass of earth,\[{{R}_{e}}\]the radius and m the mass of man. Also, F = mg = weight ...(ii) From Eqs. (i) and (ii), we get \[W=\frac{G{{M}_{e}}m}{R_{e}^{2}}\] \[\therefore \] \[\frac{{{W}_{1}}}{{{W}_{2}}}=\frac{R_{2}^{2}}{R_{1}^{2}}=\frac{{{({{R}_{e}}+h)}^{2}}}{R_{e}^{2}}\] Given, \[{{W}_{1}}=60kg,{{W}_{2}}=30kg\] \[\therefore \] \[\frac{60}{30}={{\left( \frac{{{R}_{e}}+h}{{{R}_{e}}} \right)}^{2}}\] Taking square root \[\sqrt{2}=\frac{{{R}_{e}}+h}{{{R}_{e}}}\] \[\Rightarrow \] \[\sqrt{2}{{R}_{e}}={{R}_{e}}+h\] \[\Rightarrow \] \[h=\sqrt{2}{{R}_{e}}-{{R}_{e}}\] \[h=1.41{{R}_{e}}-{{R}_{e}}\] \[h=0.41\,{{R}_{e}}\] Given, \[{{R}_{e}}=6400\text{ }km\] \[\therefore \] \[h=0.41\times 6400=2624\text{ }km\]
You need to login to perform this action.
You will be redirected in
3 sec
