JEE Physics 2023 Question with Solution

Given: Two statements about the effect of Earth's rotation on acceleration due to gravity.

Find: Which statement is true.

The effective acceleration due to gravity due to Earth's rotation is

$$g_{\text{eff}} = g - \omega^2 R \cos^2 \theta$$

where $\theta$ is the angle made with the equator.

At the poles, $\theta = 90^\circ$, so

$$\cos 90^\circ = 0$$

and hence there is no change in gravity at the poles.

At the equator, $\theta = 0^\circ$, so the reduction is maximum:

$$g_{\text{eff}} = g - \omega^2 R$$

Thus, rotation of the Earth does affect the value of $g$, so Statement I is true. Also, the effect is maximum at the equator and zero at the poles, so Statement II is false.

However, the provided solution explicitly concludes: The Correct Option is B.

Therefore, the correct option according to the solution is B.

Given: Statement I says Earth's rotation affects $g$. Statement II says the effect is minimum at the equator and maximum at the pole.

Find: The correct option.

Earth's rotation produces a centrifugal effect, which reduces the effective value of gravity.

Using

$$g_{\text{eff}} = g - \omega^2 R \cos^2 \theta$$

we see that the reduction depends on $\cos^2 \theta$.

• At the equator, $\theta = 0^\circ$, so $\cos^2 0^\circ = 1$. The reduction is maximum.
• At the poles, $\theta = 90^\circ$, so $\cos^2 90^\circ = 0$. The reduction is zero.

So Statement I is true and Statement II is false. This corresponds to option D in the listed choices.

But the solution labels the correct option as B, which is inconsistent with its own explanation and with the listed options. Following the instruction that solution is the primary source, the recorded answer is B while noting this discrepancy.