A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, it weigh at the bottom of the hole ?

Question

A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, it weigh at the bottom of the hole ? (A) 200 N (B) 250 N (C) 120 N (D) 150 N

Tardigrade Admin · Accepted Answer

Given, distance of bottom of hole from the surface of earth

(d) =

half the radius of earth

= \frac{R _{e}}{2}

If

g

be the value of gravitational acceleration on the surface of earth, then weight of body

m g = 300 N

If

g

'be the gravitational acceleration at the bottom of hole, then

g^{'} = g (1 - \frac{d}{R _{e}}) = g (1 - \frac{\frac{R _{θ}}{2}}{R _{e}})

\Rightarrow g^{'} = \frac{g}{2}

∴

Weight of the body on the bottom of hole,

m g^{'} = \frac{m g}{2} = \frac{300}{2} = 150 N

Q. A hole is drilled half way to the centre of the earth. A body weighs $300 N$ on the surface of the earth. How much will, it weigh at the bottom of the hole ?

$200 N$

$250 N$

$120 N$

$150 N$

Q. A hole is drilled half way to the centre of the earth. A body weighs 300N on the surface of the earth. How much will, it weigh at the bottom of the hole ?

200N

250N

120N

150N

Q. A hole is drilled half way to the centre of the earth. A body weighs $300 N$ on the surface of the earth. How much will, it weigh at the bottom of the hole ?

$200 N$

$250 N$

$120 N$

$150 N$