First slide

Acceleration due to gravity and its variation

Question

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)

Moderate

A

$\sqrt{\frac{g}{3 R}}$
B

$\sqrt{\frac{2 g}{3 R}}$
C

$\sqrt{\frac{3 g}{5 R}}$
D

$\sqrt{\frac{2 g}{7 R}}$

Solution

${mg}^{'} = mg - {mRω}^{2} \cos^{2} ϕ$
$Now, \frac{2}{5} mg = mg - {mRω}^{2}$
$or {mRω}^{2} = mg - \frac{2}{5} mg = \frac{3}{5} mg or ω = \sqrt{\frac{3 g}{5 R}}$

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