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7.Gravitation
medium
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 $G = 6.67 \times {10^{ - 11}}\,N{m^2}/k{g^2})$
A
$6.67 \times 10^{-9}\, J$
B
$6.67 \times 10^{-10} \,J$
C
$13.34 \times 10^{-10} \,J$
D
$3.33 \times 10^{-10} \,J$
(AIEEE-2005)
Solution
(b) Potential energy of system of two mass
$U = \frac{{ – GMm}}{R}$
$U=\frac{{ – 6.67 \times {{10}^{ – 11}} \times 100 \times 10 \times {{10}^{ – 3}}}}{{10 \times {{10}^{ – 2}}}}$
$U = – 6.67 \times {10^{ – 10}}J$
So, the amount of work done to take the particle up to infinite will be $6.67 \times {10^{ – 10}}\, J$
Standard 11
Physics
