Given below are two statement:
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 : 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
- Both statement I and statement II are false
- statement I is true but statement II is false
- Both statement I and statement II are true
- statement I is false but statement II is true
The Correct Option is B
Solution and Explanation
Understanding the effect of Earth's rotation on gravity.
Due to the rotation of the Earth, the effective acceleration due to gravity is given by: \[ g_{\text{eff}} = g - \omega^2 R \cos^2 \theta \] Where \( \theta \) is the angle made with the equator.
At the poles, where \( \theta = 90^\circ \), the change in gravity is zero because \( \cos(90^\circ) = 0 \). This shows no effect on the poles. For the equator, where \( \theta = 0^\circ \), the change in gravity is maximum: \[ g_{\text{eff}} = g - \omega^2 R \] Thus, the change in gravity is maximum at the equator and zero at the poles.
This contradicts Statement II, but Statement I is correct.
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