Question

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

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

Answer 1

Answer: (B)

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