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Question

Consider a particle of mass m suspended vertically by a string at the equator. Let R and M denote the radius and the mass of the earth respectively. If ω is the angular velocity of earth's rotation about its own axis, the tension in the string is equal to


A

GmM2R2

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B

GmMR2

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C

GmMR2mω2R

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D

GmMR2+mω2R

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Solution

The correct option is C

GmMR2mω2R


The acceleration due to gravity at a place on the surface of the earth is given by
g=gω2R cos ϕ where ϕ is the latitude of the place.
At the equator, ϕ=0. Therefore, g=gω2R
Therefore, the tension in the string will be T=mg=mgmω2R=GmMR2mω2R
Hence, the correct choice is (c).


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