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Question:

If the Earth has no rational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. radius of the Earth is 6400 km and g = 10m/s².

0.83×10⁻⁷rad/s

1.1×10⁻⁷rad/s

0.63×10⁻⁷rad/s

0.28×10⁻⁷rad/s

Solution:

The correct option is B
0.63×10⁻⁷rad/s
w=mg
mg=mω²R
3w/4w=mω²R
3w/4=mω²R
ω²R=3w/4m
ω²R=3/4g
ω=√(3g/4R)
ω=√(10/4×6400×10³)
ω=√(122×82×100²)=0.625×10⁻⁷ rad/s