Gravitation - Result Question 25
26. At what height from the surface of earth the gravitational potential and the value of $g$ are $-5.4 \times 10^{7} J kg^{-1}$ and $6.0 ms^{-2}$ respectively?
Take the radius of earth as $6400 km$ : [2016]
(a) $2600 km$
(b) $1600 km$
(c) $1400 km$
(d) $2000 km$
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Answer:
Correct Answer: 26. (a)
Solution:
- (a) As we know, gravitational potential (V) and acceleration due to gravity $(g)$ with height
$V=\frac{-G M}{(R+h)}=-5.4 \times 10^{7}$
and $g=\frac{G M}{(R+h)^{2}}=6$
Dividing (1) by (2)
$ \begin{aligned} & \Rightarrow \frac{\frac{-G M}{(R+h)}}{\frac{G M}{(R+h)^{2}}}=\frac{-5.4 \times 10^{7}}{6} \\ & \Rightarrow \quad \frac{5.4 \times 10^{7}}{(R+h)}=6 \\ & \Rightarrow \quad(R+h)=9000 km so, h=2600 km \end{aligned} $
