Question

The gravitational potential at height h above the earth's surface is $-5.12\times {10}^{7}J/kg$ and acceleration due to gravity at this point is 6.4 $m{s}^{-2}$. 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

The correct option is B 1600 km

Given that,

Gravitational potential $U=-5.12\times {10}^{7}J\setminus kg$

Acceleration due to gravity $g=6.4m/s^2$

Let r be the distance of the given point from the center of the earth.

We know that,

Gravitational potential $U=-5.12\times {10}^7=\frac{-Gm}{r}....\left(I\right)$

Acceleration due to gravity $g=6.4=\frac{Gm}{r^2}....\left(II\right)$

Now, dividing equation (I) by equation (II)

$\frac{Gm\times r^2}{Gm\times r}=\frac{5.12\times {10}^7}{6.4}$

$r=0.8\times {10}^{7}m$

$r=8000km$

Now, the height of the point from earth’s surface

$h=r-R$

$h=8000-6400$

$h=1600km$

Hence, the height is $1600km$