A particle hanging from a spring stretches it by 1 cm at earth’s surface. Radius of earth is 6400 km. At a place 800 km above the earth’s surface, the same particle will stretch the spring by:

0.79 cm

$\frac{kx_1}{kx_2}=\frac{F_{gr_1}}{F_{gr_2}}=\left(\frac{r_2}{r_1}\right)^2$

$\Rightarrow \frac{x_1}{x_2}=\left(\frac{800+6400}{6400}\right)^2=\left(\frac{72}{64}\right)^2=\left(\frac{9}{8}\right)^2$

$\Rightarrow \frac{x_1}{x_2}=\frac{81}{64}$

$\Rightarrow x_2=\frac{64}{81} x_1=\frac{64}{81}$ cm

= 0.79 cm