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Question

At what angular speed the Earth should rotate, so that effective acceleration due to gravity at 45∘ latitude becomes half of effective acceleration due to gravity at pole? (Radius of earth is R and acceleration due to gravity without taking variation of Earth’s rotation at surface is β€˜gβ€²)

A
ω=gR
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B
ω=g2R
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C
ω=2gR
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D
ω=3g4R
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Solution

The correct option is A ω=gR

g=gRw2cos2ϕ

given g45=12×g90


g45=gRω2×12

g90=g

gω2R2=12×g

ω2R2=g2

Hence ω=gR


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