An object of mass 100 kg falls from point $A$ to $B$ as shown in figure. The change in its weight co

Question

An object of mass 100 kg falls from point $A$ to $B$ as shown in figure. The change in its weight corrected to the nearest integer is ( $R_E$ is the radius of the earth)

Professor PC Thomas Classes · Answer

(a) : Given, $m=100 \mathrm{~kg}, g=10 \mathrm{~m} / \mathrm{s}^2$
$W_A=m g_A=m g\left(\frac{R_{\mathrm{E}}}{R_E+H_B}ight)^2=m g\left(\frac{R_E}{R_E+2 R_E}ight)^2=\frac{m g}{9}$
$W_B=m g_B=m g\left(\frac{R_{\mathrm{E}}}{R_E+H_B}ight)^2=m g\left(\frac{R_E}{R_E+\frac{3 R_E}{2}}ight)^2=\frac{4 m g}{25}$
Change in weight $=W_B-W_A$
$\begin{aligned} & =\frac{4 m g}{25}-\frac{m g}{9}=\frac{36 m g-25 m g}{225} \ & =\frac{11 m g}{225}=\frac{11}{225} 	imes 100 	imes 10=49 \mathrm{~N}\end{aligned}$