Gravitation Question 362
Question: At what height from the surface of earth the gravitational potential and the value of g are$ [-5.4\times 10^{7}J k{{g}^{-1}} and 6.0 m{{s}^{-2}}] $ respectively? Take the radius of earth as 6400 km:
Options:
A) 2600 km
B) 1600 km
C) 1400 km
D)2000 km
Show Answer
Answer:
Correct Answer: A
Solution:
-
As we know, gravitational potential (v) and acceleration due to gravity (g) with height
$ [V=\frac{-GM}{R+H}=5.4\times 10^{7}] $ -(i) And
$ [g=\frac{GM}{\left( R+H \right)}=6] $ …(ii) Dividing (i) by (ii)
$ [\frac{\frac{-GM}{R+H}}{\frac{GM}{{{\left( R+H \right)}^{2}}}}=\frac{-5.4\times 10^{7}}{6}\Rightarrow \frac{5.4\times 10^{7}}{\left( R+H \right)}=6] $
$ [\Rightarrow R+h=9000km,so,h=2600k] $
