GravitationMedium
Question
The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is shown in figure below
(1)
(2)
(3)
(4)
The correct figure is
(1)
(2)(3)
(4)The correct figure is
Options
A.(4)
B.(1)
C.(2)
D.(3)
Solution
The acceleration due to gravity at a depath d below surface of earth is
g′ = 0 at d = R
i.e., acceleration due to gravity is zero at the centre of earth.
Thuus, the variation in value of g with r is
For r > R,
⇒ g′ ∝ 
Here, R + h = r
For r < R, g′ = g
Here, R - d = r ⇒ g′ ∝ r
Therefore, the variation of g with distace from centre of the earth will be as shown in the figure.
g′ = 0 at d = R
i.e., acceleration due to gravity is zero at the centre of earth.
Thuus, the variation in value of g with r is
For r > R,
⇒ g′ ∝ Here, R + h = r
For r < R, g′ = g
Here, R - d = r ⇒ g′ ∝ r
Therefore, the variation of g with distace from centre of the earth will be as shown in the figure.
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