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. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Effective acceleration due to gravity $g^{\prime }=g-R{w}^{2}si{n}^2\lambda$ where $\lambda$ is the lattitude angle

At equator $\lambda ={90}^o$ $⟹g_e^{\prime }=g-R{w}^2$ $(sin{90}^o=1)$

At poles $\lambda =0^o$ $⟹g_p^{\prime }=g$ $(sin{0}^o=0)$

$\therefore$ $g_p^{\prime }-g_e^{\prime }=g-(g-R{w}^2)=R{w}^2$

$⟹$ $g_p^{\prime }-g_e^{\prime }\propto w^2$

Hence, Assertion is correct.

Acceleration due to gravity at the surface of earth $g=\frac{GM}{R^2}$

But $R_p<R_e$ $⟹g_p>g_e$

Hence, the reason statement is also correct but it does not explain the assertion correctly.