Gravitation Question 72
Question: If earth is supposed to be a sphere of radius R, if g30 is value of acceleration due to gravity at latitude of 30o and g at the equator, the value of $ [g-{g_{30^{o}}}] $ is [DCE 2005]
Options:
A) $ [\frac{1}{4}{{\omega }^{2}}R] $
B) $ [\frac{3}{4}{{\omega }^{2}}R] $
C) $ [{{\omega }^{2}}R] $
D) $ [\frac{1}{2}{{\omega }^{2}}R] $
Show Answer
Answer:
Correct Answer: B
Solution:
Acceleration due to gravity at latitude l is given by
$ [{g}’=g-R{{\omega }^{2}}{{\cos }^{2}}\lambda ] $
At $ [30^{o},{g_{30{}^\circ }}=g-R{{\omega }^{2}}{{\cos }^{2}}30^{o}=g-\frac{3}{4}R{{\omega }^{2}}] $
$ [g-g_{30}=\frac{3}{4}{{\omega }^{2}}R.] $
