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,
$g^{\prime }=g-R_e{\omega }^{2}co{s}^2\lambda$
At equator, $\lambda =0^{\circ }$,
$\therefore cos{0}^{\circ }=1$
$\therefore g_e-g-R_e{\omega }^2$
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.