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 earths surface, the same particle will stretch the spring by

• A. $0.79cm$
• B. $1.2cm$
• C. $4cm$
• D. $17cm$

Answer 1

The correct option is A $0.79cm$

as, $mg=kx$

where, $x=1cm,k=$spring constant

for second case $m{g}^{\prime }=k{x}^{\prime }$

Hence $\frac{g}{g^{\prime }}=\frac{x}{x^{\prime }}$

$x^{\prime }=x{g}^{\prime }/g$

$x^{\prime }=\frac{xg{R}^2}{(R+h{)}^{2}g}$

Earth's radius, $R=6400$

At height, $h=800$

$x^{\prime }=\frac{1\times (6400\times {10}^3{)}^2}{(7200\times {10}^3{)}^2}$

$x^{\prime }=0.79cm$