Question

The gravitational potential at height h above the earth's surface is $-5.12\times 10^{7}\,J\,kg^{- 1}$ and acceleration due to gravity at this point is $6.4\,ms^{- 2}.$ If radius of the earth is $6400\,km$ the value of $h$ is :-

• A. $1200\,km$
• B. $1600\,km$
• C. $1800\,km$
• D. $2400\,km$

Answer 1

Answer: (B)

Gravitational potential,
$V=\frac{GM}{R + r}$
Also, $g^{'}=\frac{GM}{\left(R + h\right)^{2}}$
Now,
$V=-\frac{GM}{\left(R + h\right)^{2}}\left(R + h\right)=-g^{'}\left(R + h\right)$
$\therefore -5.12\times \left(10\right)^{7}=-6.4\left(6400 + h\right)\times \left(10\right)^{3}$
Solving we get; $h=1600\,km$