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Questions  

What should be the angular velocity of rotation of the earth about its own axis so that the weight of a body at the equator reduces to 2/5 of its present value? (Take R as the radius of the earth)

a
g3R
b
2g3R
c
3g5R
d
2g7R

detailed solution

Correct option is C

mg′=mg−mRω2cos2⁡ϕ Now, 25mg=mg−mRω2 or mRω2=mg−25mg=35mg or ω=3g5R

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The angular speed of earth, so that the object on equator may appear weightless, is (g=10m/s2, radius of earth 6400 km)


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