Gravitation Question 67

Question:What should be the angular speed of earth, so that body lying on equator may appear weightlessness $ [(g=10m/s^{2},R=6400km)] $ [Pb. PET 2000]

Options:

A) $ [\frac{1}{800}rad/s] $

B) $ [\frac{1}{400}rad/s] $

C) $ [\frac{1}{600}rad/s] $

D) $ [\frac{1}{100}rad/s] $

Show Answer

Answer:

Correct Answer: A

Solution:

$ [{g}’=g-{{\omega }^{2}}R{{\cos }^{2}}\lambda ] $

For weightlessness at equator $ [\lambda =0{}^\circ ] $ and $ [g’=0] $

$ [0=g-{{\omega }^{2}}R] $

Þ $ [\omega =\sqrt{\frac{g}{R}}=\frac{1}{800}\frac{rad}{\sec }] $



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