Question

A body weighs 250 N on the surface of the earth. How much will it weigh half way down to the centre of the earth ?

• A. 125 N
• B. 150 N
• C. 175 N
• D. 250 N

Answer 1

Answer: (A)

125 N

Answer 2

Let m be mass of a body.

$\therefore$Weight of the body on the surface of the earth is

W = mg = 250N

Accelerations due to gravity at a depth d below the surface of the earth is

Weight of the body at depth d is

W`=mg` = mg

Here, $d = \frac { R _ { E } } { 2 }$

$\therefore$ $\mathrm { W } = \mathrm { mg } \left( 1 - \frac { \mathrm { R } _ { \mathrm { E } } / 2 } { \mathrm { R } _ { \mathrm { E } } } \right) = \frac { \mathrm { mg } } { 2 } = \frac { \mathrm { W } } { 2 } = \frac { 250 \mathrm {~N} } { 2 } = 125 \mathrm {~N}$