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.

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (B)

Acceleration due to gravity,
$g'=g-R_{e}\omega^{2} cos^{2}\lambda$
At equator, $\lambda=0^{\circ}$,
$ \therefore cos0^{\circ}=1$
$\therefore \, g_e-g-R_{e } \omega^{2}$
At poles, $\lambda=90^{\circ}$,
$ \therefore \, cos90^{\circ}=0 \,$
$\therefore g_{p}=g$
Thus, $g_{p}-g_{e}=g-g+R_{e}\omega^{2}=R_{e}\omega^{2}$
Also, the value of $g$ is maximum at poles and minimum at equator.