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Question

What should be the angular speed with which the earth have to rotate on its axis so that a person on the equator would weigh 35 as much as present ?

A
2g5R
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B
5g2R
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C
gR
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D
7g2R
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Solution

The correct option is A 2g5R
The acceleration due to gravity g considering the effect of rotation at the equator is given by

g=g(1ω2R)

where,
ω= angular velocity of the Earth
R= is the radius of the Earth

Hence, the weight is given by

mg=mgmω2R

From question, mg=35mg

35mg=mgmω2R

25mg=mω2R

ω=2g5R

Hence, option (a) is correct

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