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

Answer 1

(a)

The acceleration due to gravity at depth his given as,

g h =( 1− 2h R e )

where, Radius of earth is R e .Acceleration due to gravity on the surface of the earth is g.

Thus the above equation shows that acceleration due to gravity decreases with an increase in the altitude.

(b)

The acceleration due to gravity at depth his given as follows,

g d =( 1- d R e )g

where, depth from earth surface is d.

Thus it is clear from the above relation that acceleration due to gravity decreases with an increase in depth.

(c)

Acceleration due to gravity of body of mass mis given as,

g= GM R 2

where, universal gravitational constant is G, mass of earth is Mand radius of earth is R.

Thus the above equation shows that acceleration due to gravity is independent of mass of the body.

(d)

The difference in potential energy at radius r 1 and r 2 is given as,

v=−GmM( 1 r 2 − 1 r 1 )

Thus, this formula is more accurate than the formula mg( r 2 -r 1 ).