Question

A body weight 144 N at the surface of earth. When it is taken to a height of h = 3R,where R is radius of earth it would weight.

• A. 48 N
• B. 36 N
• C. 16 N
• D. 9 N

Answer 1

The correct option is D 9 N

Given that,

Weight of body $W=144N$

Height $h=3R$

Radius of earth $=R$

We know that,

Acceleration due to gravity at the surface of the earth $=g$

Acceleration due to gravity at height $g^{\prime }=3R$

Now,

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

$\frac{g}{g^{\prime }}={\left(\frac{R}{R+3R}\right)}^2$

$\frac{g}{g^{\prime }}=\frac{1}{16}$

Now, weight at the height

$\frac{w^{\prime }}{w}=\frac{m{g}^{\prime }}{mg}$

$\frac{w^{\prime }}{w}=\frac{1}{16}$

$w^{\prime }=\frac{w}{16}$

$w^{\prime }=\frac{144}{16}$

$w^{\prime }=9N$

Hence, the weight at the height is $9N$