### JEE Main On 8 April 2017 Question 7

##### Question: If the earth has no rotational motion, the weight of a person on the equation is W. Detrmine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $ \frac{3}{4}W. $ Radius of the earth is 6400 km and $ g=10m/s^{2}. $ [JEE Online 08-04-2017]

#### Options:

A) $ 0.63\times {10^{-3}}rad/s $

B) $ 0.28\times {10^{-3}}rad/s $

C) $ 1.1\times {10^{-3}}rad/s $

D) $ 0.83\times {10^{-3}}rad/s $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- $ g’=g-{{\omega }^{2}}R{{\cos }^{2}}\theta $ $ \frac{3g}{4}=g-{{\omega }^{2}}R $ $ w^{2}R=\frac{g}{4} $ $ w=\sqrt{\frac{g}{4R}} $ $ =\sqrt{\frac{10}{4\times 64\omega \times 10^{3}}} $ $ =\frac{1}{2\times 8\times 100} $ $ =\frac{1}{1600}=\frac{1}{16}\times {10^{-2}}=0.6\times {10^{-3}} $