Gravitation Question 80
Question: Assertion: The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth. Reason: The value of acceleration due to gravity is minimum at the equator and maximum at the pole.
Options:
A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
C) If assertion is true but reason is false.
D) If the assertion and reason both are false.
E) If assertion is false but reason is true.
Show Answer
Answer:
Correct Answer: B
Solution:
Acceleration due to gravity, $ [{g}’=g-R{{\omega }^{2}}{{\cos }^{2}}\lambda ] $ At equator, $ [\lambda =0{}^\circ ] $ i.e. $ [\cos 0{}^\circ =1] $ \ $ [g_{e}=g=R{{\omega }^{2}}] $ At poles, $ [\lambda =90{}^\circ ] $ i.e. $ [\cos 90{}^\circ =0] $ \ $ [g_{p}=g] $ Thus, $ [g_{p}-g_{e}=g-g+R{{\omega }^{2}}=R{{\omega }^{2}}] $ Also, the value of g is maximum at poles and minimum at equators.
