__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/*r*_{2}– 1/*r*_{1}) is more/less accurate than the formula*mg*(*r*_{2}–*r*_{1}) for the difference of potential energy between two points*r*_{2}and*r*_{1}distance away from the centre of the earth.

__Solution__:**(a)**Decreases

Acceleration due to gravity at depth

*h*is given by the relation:

g

_{h}= [1 - (2h / R

_{e})]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.

**(b)**Decreases

Acceleration due to gravity at depth

*d*is given by the relation:

g

_{d}= [1 - (d / R

_{e})]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 / 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 of the body.

**(d)**More

Gravitational potential energy of two points

*r*

_{2}and

*r*

_{1}distance away from the centre of the Earth is respectively given by:

V(r

_{1}) = -GmM / r

_{1}

V(r

_{2}) = -GmM / r

_{2}

∴ Difference in potential energy, V = V(r

_{2}) - V(r

_{1}) = -GmM [ (1 / r

_{2}) - (1 / r

_{1}) ]

Hence, this formula is more accurate than the formula

*m*g(

*r*

_{2}–

*r*

_{1}).

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