Question

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

• A. $1cm$
• B. $8cm$
• C. $0.1cm$
• D. $0.79cm$

Answer 1

The correct option is D $0.79cm$

In first case,

${Kx}_1=m{g}_0$

$K=\frac{{mg}_0}{1cm}=100\left({mg}_0\right)$ N/m

At height $h=800$ Km

$g=g_0(1-\frac{2h}{R})$

$g=g_0(1-\frac{2\times 800}{6400})$

$g=\frac{3g_0}{4}$

Now,

for second case

${Kx}_2=mg$

$\left(100\right){mg}_0\left(x_2\right)=m\left(\frac{3g_0}{4}\right)$

$x_2=\frac{3}{4}cm$

$x_2=0.79cm$