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If the earth has no rotational 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 weight is 23W . [Radius of earth =6400 km and g=10m / s2]

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a

1.1×103rad/sec

b

0.93×10−5rad/sec

c

0.72×10−3rad/sec

d

0.58×10−3rad/sec

answer is C.

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Detailed Solution

g1=g−ω2Rcos2θ ⇒2g3=g−ω2R ⇒ω2R=g−2g3=3g−2g3 ⇒ω2R=g3 ⇒ω=g3R ⇒ω=103×6400×103 ⇒ω=180×103=0.72×10−3rad/sec

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If the earth has no rotational 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 weight is 23W . [Radius of earth =6400 km and g=10m / s2]