Question

A particle hanging from a spring stretches by $1cm$ at earth's surface. At a point $800km$ above earths surface, the same spring stretches by the same particle (Radius of earth $R=6400km$) is:

• A. $1cm$
• B. $0.75cm$
• C. $1.2cm$
• D. $1.4cm$

Answer 1

The correct option is B $0.75cm$

Given,

Let the mass of the body be $m$, and the gravitational acceleration $g_o$ stretches in spring$1cm$,

The height above the earth's surface$=800Km$

Radius of the earth $R=6400Km$

So,

$m{g}_o=-k{x}_1$..................(1)

We know that,

$g^{\prime }=g_o\left(1-\frac{2h}{R}\right)$

$m{g}^{\prime }=-k{x}_2$................(2)

from equaiton$\left(1\right)$ and $\left(2\right)$

$\frac{4}{3}=\frac{1}{x_2}$

So $x_2=0.75cm$