Question

# The work done in shifting a particle of mass m from the centre of earth to the surface of the earth is

A
mgR
B
12mgR
C
zero
D
mgR
Solution
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#### Given,The mass of the particle be m,Initilly it is on the centre of the earth, soThe work done in moving a particle from center of earth to its surface W=∫R0Fdr=∫R0(−G(ρ43πr3)mr2)dr=∫R0(−4Gρπmr3)dr=GMm2R,we know that F=GMmR2=mg=12mgR(Since g=GMR2)So, The work done in shifting a particle of mass from the centre of the earth to the surface of the earth is =mgR2.

4
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