Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.2

Question 8.2:
Choose the correct alternative:
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth. (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula –G Mm(1/r2– 1/r1) is more/less accurate than the formula mg(r2r1) for the difference of potential energy between two points r2and r1distance away from the centre of the earth.
Solution:
(a) Decreases
Acceleration due to gravity at depth h is given by the relation:
gh = [1 - (2h / Re)]g
Where,
Re = Radius of the Earth
g = Acceleration due to gravity on the surface of the Earth
It is clear from the given relation that acceleration due to gravity decreases with an increase in height.

(b) Decreases
Acceleration due to gravity at depth d is given by the relation:
gd = [1 - (d / Re)]g
It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.

(c) Mass of the body
Acceleration due to gravity of body of mass m is given by the relation:
g = GM / R2
Where,
G = Universal gravitational constant
M = Mass of the Earth
R = Radius of the Earth
Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.

(d) More
Gravitational potential energy of two points r2 and r1 distance away from the centre of the Earth is respectively given by:
V(r1) = -GmM / r1
V(r2) = -GmM / r2
∴ Difference in potential energy, V = V(r2) - V(r1) = -GmM [ (1 / r2) - (1 / r1) ]

Hence, this formula is more accurate than the formula mg(r2r1).

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