Question

The radius of the earth is $6400km$ and $g=10{ms}^{-2}$. In order that the body of $5kg$ weighs zero at the equator, the angular speed of the earth should be:

• A. $\frac{1}{80}{rads}^{-1}$
• B. $\frac{1}{400}{rads}^{-1}$
• C. $\frac{1}{800}{rads}^{-1}$
• D. $\frac{1}{1600}{rads}^{-1}$

Answer 1

The correct option is C $\frac{1}{800}{rads}^{-1}$

There is a relationship for a body to be weightless at the equator. Relationship is given by $W=\sqrt{\frac{g}{R}}$. Where $W$ is angular speed $g$ is acceleration due to gravity $R$ is radius of the earth substituting the given values in a above equation.

$6400km=6400\times {10}^{3}m$

$W=\sqrt{\frac{10}{6400\times {10}^3}}$

$W=\sqrt{\frac{1}{640000}}$

$=\frac{1}{800}rad/s$.