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.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Assertion is correct but Reason is incorrect
Both Assertion and Reason are incorrect
A
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
B
Both Assertion and Reason are incorrect
C
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
D
Assertion is correct but Reason is incorrect
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Solution
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Effective acceleration due to gravity g′=g−Rw2sin2λ where λ is the lattitude angle
At equator λ=90o⟹g′e=g−Rw2(sin90o=1)
At poles λ=0o⟹g′p=g(sin0o=0)
∴g′p−g′e=g−(g−Rw2)=Rw2
⟹g′p−g′e∝w2
Hence, Assertion is correct.
Acceleration due to gravity at the surface of earth g=GMR2
But Rp<Re⟹gp>ge
Hence, the reason statement is also correct but it does not explain the assertion correctly.
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