Gravitation

JEE Main level, single correct, medium

58 of 223

Question 58 of 223

Given below are two statements:
Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)(g).
Statement II : The effect of rotation of the earth on the value of gg 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

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Answer: (D) Statement I is true but statement II is false

The variation of acceleration due to gravity with the rotation of Earth can be written as
g′=g−ω2Rcos⁡2λ...(1)g'=g-{\omega }^{2}R{\cos }^{2}\lambda ...\left(1\right)
Substitute 0∘0^{\circ} for λ\lambda for equatorial position to obtain the acceleration due to gravity.
g′=g−ω2Rcos⁡20∘=g−ω2R\begin{matrix}g' & = & g-{\omega }^{2}R{\cos }^{2}0^{\circ} \\ & = & g-{\omega }^{2}R\end{matrix}
Substitute 90∘90^{\circ} for λ\lambda for polar position to obtain the acceleration due to gravity.
g′=g−ω2Rcos⁡290∘=g\begin{matrix}g' & = & g-{\omega }^{2}R{\cos }^{2}90^{\circ} \\ & = & g\end{matrix}
The above two equations show that the effect on acceleration due to gravity is maximum at the equator and minimum at pole.

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