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If earth were to rotate on its own axis such that the weight of a person at the equator becomes half the weight at the poles, then its time period of rotation is (g = acceleration due to gravity near the poles and R is the radius of earth) (Ignore equatorial bulge) [EAMET 2013]

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a

2π2Rg

b

2πR2g

c

πR3g

d

2πRg

answer is A.

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Detailed Solution

Here, g0=g'-Rω2Given, g0=g2 and g'=gSo, g2=g-Rω2⇒ω=g2RWe have, T=2πrv⇒T=2πω ∵ω=vrHence, T=2π2Rg

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If earth were to rotate on its own axis such that the weight of a person at the equator becomes half the weight at the poles, then its time period of rotation is (g = acceleration due to gravity near the poles and R is the radius of earth) (Ignore equatorial bulge) [EAMET 2013]