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Question: Find the velocity of the earth at which it should rotate so that weight of a body becomes zero at th...

Find the velocity of the earth at which it should rotate so that weight of a body becomes zero at the equator.

A

1.25 rad s-1

B

1.25 × 10-1 rad s-1

C

1.25 × 10-2 rad s-1

D

1.25 × 10-3 rad s-1

Answer

1.25 × 10-3 rad s-1

Explanation

Solution

g' = g (1−Rω2g)=0\left( 1 - \frac{R\omega^{2}}{g} \right) = 0or ω = gR\sqrt{\frac{g}{R}}

= 106400×103=1800=1.25×10−3rads−1\sqrt{\frac{10}{6400 \times 10^{3}}} = \frac{1}{800} = 1.25 \times 10^{- 3}rads^{- 1}