A body weighs 200 N on the surface of the earth How much will it weigh half way down to the centre of the earth ?

Question

A body weighs 200 N on the surface of the earth How much will it weigh half way down to the centre of the earth ? (A) 250 N (B) 100 N (C) 150 N (D) 200 N

Tardigrade Admin · Accepted Answer

Acceleration due to gravity at a depth d from surface of earth

g^{'} = g (1 - \frac{d}{R})

...(1)
Where g = acceleration due to gravity at earth's surface
Multiplying by mass 'm' on both sides of (1)

m g^{'} = m g (1 - \frac{d}{R}) (d = \frac{R}{2})

= 200 (1 - \frac{R}{2 R}) = \frac{200}{2} = 100 N

Q. A body weighs 200N on the surface of the earth How much will it weigh half way down to the centre of the earth ?

250 N

100 N

150 N

200 N

Acceleration due to gravity at a depth d from surface of earth g′=g(1−Rd​) ...(1) Where g = acceleration due to gravity at earth's surface Multiplying by mass 'm' on both sides of (1) mg′=mg(1−Rd​)(d=2R​) =200(1−2RR​)=2200​=100N

Q. A body weighs $200 N$ on the surface of the earth How much will it weigh half way down to the centre of the earth ?