Question

$W$ is the weight of a man on the surface of the earth. What would be his weight $\left(W\right)$ if he goes to a height $\left(h\right)$ equal to radius of the earth, from the surface of the earth?

• A. $W=\frac{W}{2}$
• B. $W=\frac{W}{3}$
• C. $W=\frac{W}{4}$
• D. $W=2W$

Answer 1

The correct option is C $W=\frac{W}{4}$

Given that,

Weight = $W$

Height = $R$

We know that,

Weight is inversely proportional to square of distance between man and center of earth

Then, initial distance is $R$ and initial weight is $W$ and when it is at height $R$ then distance is $2R$

Now,

$W\propto \frac{1}{d^2}$

Now,

$\frac{W_1}{W_2}={\left(\frac{d_2}{d_1}\right)}^2$

$\frac{W_1}{W_2}={\left(\frac{2R}{R}\right)}^2$

$\frac{W_1}{W_2}=\frac{4R^2}{R^2}$

$\frac{W}{W_2}=4$

$W_2=\frac{W}{4}$

Hence, the weight at height is $\frac{W}{4}$