Question

A body of weight $1N$ is placed at the surface of the earth, which is assumed to be a perfect sphere of radius $6400km$ . It is taken to a height of $600km$ , the weight of the body, in $N$ , would be :

• A. $13/16$
• B. $(3/32{)}^2$
• C. $(32/35{)}^2$
• D. $1$

Answer 1

The correct option is A $13/16$

Acceleration due to gravity at height $h$ is given by:

$g^{\prime }=g\left(1-\frac{2h}{R}\right)$

$g^{\prime }=g\left(1-\frac{2\times 6\times {10}^5}{6.4\times {10}^6}\right)$

$\frac{g^{\prime }}{g}=\left(1-\frac{1.2}{6.4}\right)$ \

$\frac{g^{\prime }}{g}=\left(1-\frac{3}{16}\right)$

$\frac{g^{\prime }}{g}=\frac{13}{16}$

New weight $W^{\prime }=m{g}^{\prime }$

$W^{\prime }=mg\times \frac{13}{16}$

$=\frac{13}{16}N$