First slide

Variation of g

Question

The angular velocity of the earth about its polar axis so that the weight of the body at the equator will be zero is

Easy

A

1.25 × 10^-3 rad s^-1
B

2 rad s^-1
C

1 rad s^-1
D

0

Solution

$\large {g_\phi } = g - R{\omega ^2}{\cos ^2}\phi$
$\large \Rightarrow 0 = g - {R^2}{\omega ^2} \Rightarrow \omega = \sqrt {\frac{g}{R}}$
Now g = 10 m/s² and R = 6400 km = 64 x 10⁵ m/s²ω = 1.25 x 10^-3 rad/sec

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