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 }] $
