Question

The weight of a body on the surface of the earth is 12.6 N. When it is raised to a height half the radius of the earth, its weight will be

• A. $2.8N$
• B. $5.6N$
• C. $12.5N$
• D. $25.2N$

Answer 1

The correct option is B

$5.6N$

Step 1: Given information

Weight of the body on the surface of the earth$\left(W_o\right)$$=12.6N$

Radius of earth$\left(R\right)$= $6.3781\times {10}^{6}m$

Half of the radius of earth$\left(h\right)$= $3.18905\times {10}^{6}m$ or $\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Step 2: Draw a diagram

Step 3: Calculate weight$\left(W\text{'}\right)$

Weight of the body at a height$\left(h\right)$,

$W\text{'}=W_o{\left(\frac{R}{R+h}\right)}^2$

$$\begin{gathered} \Rightarrow W\text{'}=12.6{\left(\frac{R}{{\displaystyle \raisebox{1ex}{$R+R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\right)}^2 \\ \Rightarrow W\text{'}=12.6\times \frac{4}{9} \\ \Rightarrow W\text{'}=5.6N \end{gathered}$$

Hence, the correct option is (B).