Gravitation Ques 22
22. 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: 22.(a)
Solution:
- (a) As we know, gravitational potential (V) and acceleration due to gravity $(g)$ with height
$V=\frac{-G M}{(R+h)}=-5.4 \times 10^{7}$ $\quad$ …….(1)
and $g=\frac{G M}{(R+h)^{2}}=6$ $\quad$ …….(2)
Dividing (1) by (2)
$ \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 $ $km$
BETA
