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Gravitation — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsGravitation1 Mark
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.
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Answer

(b) Acceleration due to gravity,$g^{\prime}=g-R \omega^2 \cos ^2 \lambda$At equator, $\lambda=0^{\circ}$ i.e. $\cos 0^{\circ}=1 \therefore g_e=g=R \omega^2$At poles, $\lambda=90^{\circ}$ i.e. $\cos 90^{\circ}=0 \therefore g_p=g$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.

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