Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below

Statement I is true but statement II is false

Statement I is false but statement II is true

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Gravitation PYQ — JEE Main 2023 · 10 Apr · Shift 2 · Q54 with Solution

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Correct answer: B

Because the Earth rotates, a body on its surface experiences a centrifugal effect.

At latitude $\lambda$ , the effective acceleration due to gravity is reduced by the component of centrifugal acceleration:

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

where:

So, the rotation of the Earth does affect the value of acceleration due to gravity.

Hence, Statement I is true.

From

$\Delta g = \omega^2 R \cos^2 \lambda$

the reduction in $g$ due to rotation depends on $\cos^2 \lambda$ .

$\cos^2 0^\circ = 1$

So the reduction is maximum.

$\cos^2 90^\circ = 0$

So the reduction is minimum (zero).

Therefore, Statement II says the opposite of the correct fact.

Hence, Statement II is false.

The correct option is:

$\boxed{\text{B}}$