The radius of the earth is 6400 km and g

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The radius of the earth is $6400\, km$ and $g = 10\,m/{\sec ^2}$. In order that a body of $5 \,kg$ weighs zero at the equator, the angular speed of the earth is

A

$1/80\, radian/sec$

B

$1/400 \,radian/sec$

C

$1/800\, radian/sec$

D

$1/1600\, radian/sec$

The radius of the earth is $6400\, km$ and $g = 10\,m/{\sec ^2}$. In order that a body of $5 \,kg$ weighs zero at the equator, the angular speed of the earth is

For the condition of weightlessness at equator $\omega = \sqrt {\frac{g}{R}} $

$\omega = \sqrt {\frac{1}{{640 \times {{10}^3}}}} = \frac{1}{{800}} \,rad/s$