GravitationHard
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.
Create a free account to view solution
View Solution FreeMore Gravitation Questions
A hydrogen balloon released on the moon would:-...The angular speed of earth in rads/s, so that bodies on equator may apper weightless is : [Use g = 10m/ s2 and the radiu...The magnitudes of gravitational field at distance r1 and r2 from the centre of a uniform sphere of radius R and mass M a...The value of acceleration due to gravity , at earth surface is g. Its value at the centre of the, which we assume as a s...The condition for a uniform spherical mass m of radius r to be a black hole is :- (G = gravitational constant and g = ac...