Gravitation Question 173
Question: A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $ [G=6.67\times {{10}^{-11}}Nm^{2}/kg^{2})] $ [AIEEE 2005]
Options:
A) $ [6.67\times 10^{9}J] $
B)$ [6.67\times 10^{10}J] $
C) $ [13.34\times 10^{10}J] $
D) $ [3.33\times 10^{10}J] $
Show Answer
Answer:
Correct Answer: B
Solution:
Potential energy of system of two mass $ [U=\frac{-GMm}{R}] $ = $ [\frac{-6.67\times {{10}^{-11}}\times 100\times 10\times {{10}^{-3}}}{10\times {{10}^{-2}}}] $
$ [U=-6.67\times {{10}^{-10}}J] $
So, the amount of work done to take the particle up to infinite will be $ [6.67\times {{10}^{-10}}] $ J
