Question

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  \(\frac{1}{r_2 }– \frac{1}{r_1}\)  is more/less accurate than the formula mg(r₂ – r₁) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth.

Answer 1

(a) Decreases, 
Acceleration due to gravity at depth h is given by the relation: g_h (\((1- \frac{2h}{Re} ) g\)
Where, 
R_e= 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.

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(b) Decreases,
Acceleration due to gravity at depth d is given by the relation: 
g_d \((1-\frac{d}{R_e})g\)

It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.

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(c) Mass of the body,
Acceleration due to gravity of body of mass m is given by the relation:
\(g =\frac{GM }{R_2}\)
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 body.

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(d) More,
Gravitational potential energy of two points Earth is respectively given by:

V(r₁) = -\(\frac{GmM }{r_1}\)
V(r₂) = - \(\frac{GmM }{r_2}\)
∴ Difference in potential energy, \(V = V(r_2) - V(r_1) = -GmM (\frac{1}{r_2 }- \frac{1}{r_1})\)

Hence, this formula is more accurate than the formula mg(r₂– r₁).