Gravitation

JEE Main level, single correct, medium

63 of 223

Question 63 of 223

Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below

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Answer: (C) Statement I is true but Statement II is false

Acceleration due to gravity is the acceleration acquired by a freely falling object.
At any particular place on the Earth, the acceleration due to gravity depends on the latitude of the place and the angular frequency of Earth's rotation. Mathematically, the latitude dependence of acceleration due to gravity can be written as
geff=g−Rω2cos⁡2λ.................(1){g}_{eff}=g-R{\omega }^{2}{\cos }^{2}\lambda .................(1)
where, geff{g}_{eff} is the effective acceleration due to gravity, gg is the real value of gravity at the latitude without considering earth rotation, RR is the radius of Earth, ω\omega is the angular frequency of rotation and λ\lambda is the latitude of the place.
According to equation (1), the value of the acceleration due to gravity varies from place to place.
The variation of acceleration due to gravity with the depth can be written as
gd=g(1−dR)....................(2){g}_{d}=g\left(1-\dfrac{d}{R}\right)....................(2)
where, gd{g}_{d} is the acceleration due to gravity at a depth dd from the surface and gg is the acceleration due to gravity at the surface.
From equation (2), it can be stated that the acceleration due to gravity decreases with the depth.
Hence, Statement I is true, but statement II is false.

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