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

1)1.25×10^-3

2)2 rad s^-1

3)1 rad s^-1

4)0
​

Answer 1

The angular velocity of the earth is $1.25\times10^{-3}\ rad/s$

(1) is correct option.

Explanation:

Given that,

The weight of the body at the equator will be zero.

We need to calculate the angular velocity of the earth

The weight of the body at the equator is given by

$W'=mg'$

$W'=m(g-R\omega^2\cos^2\phi)$

$mg'=m(g-R\omega^2\cos^2\phi)$

$g'=g-R\omega^2\cos\phi$

At the equator,

$\phi=0$

So,

$g'=(g-R\omega^2)$...(I)

For weight to be zero

So,

$g'=0$

Put the value in the equation (I)

$g-R\omega^2=0$

$\omega^2=\dfrac{g}{R}$

Put the value into the formula

$\omega^2=\dfrac{9.8}{6400\times10^{5}}$

$\omega=\sqrt{1.53\times10^{-8}}$

$\omega = 1.25\times10^{-3}\ rad/s$

Hence, The angular velocity of the earth is $1.25\times10^{-3}\ rad/s$

Learn more :

Topic : angular velocity

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