Gravitation Question 111
Question: In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $ [(g=10,m{{s}^{-2}}] $ and radius of earth is 6400 kms) [Roorkee 2000]
Options:
A) $ [0,\ rad,{{\sec }^{-1}}] $
B)$ [\frac{1}{800}rad,se{{c}^{-1}}] $
C) $ [\frac{1}{80}rad,se{{c}^{-1}}] $
D)$ [\frac{1}{8}rad,se{{c}^{-1}}] $
Show Answer
Answer:
Correct Answer: B
Solution:
$ [{g}’=g-{{\omega }^{2}}R{{\cos }^{2}}\lambda ,] $ For weightlessness at equator $ [\lambda =0] $ and $ [g’=0] $ \ $ [0=g-{{\omega }^{2}}R] $ Þ $ [\omega =\sqrt{\frac{g}{R}}=\frac{1}{800}\ \frac{rad}{s}] $
BETA
