Gravitation Question 5
Question 5 - 2024 (29 Jan Shift 1)
At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)
(1) $\sqrt{5} R-R$
(2) $\frac{\sqrt{3} R-R}{2}$
(3) $\frac{R}{2}$
(4) $\frac{\sqrt{5} R-R}{2}$
Show Answer
Answer: (4)
Solution:
$g _p=\frac{g R^{2}}{(R+h)^{2}}$
$g _q=g\left(1-\frac{h}{R}\right)$
$g _p=g _q$
$\frac{g}{\left(1+\frac{h}{R}\right)^{2}}=g\left(1-\frac{h}{R}\right)$
$\left(1-\frac{h^{2}}{R^{2}}\right)\left(1+\frac{h}{R}\right)=1$
Take $\frac{h}{R}=x$
So
$x^{3}-x+x^{2}=0$
$x=\frac{\sqrt{5}-1}{2}$
$h=\frac{R}{2}(\sqrt{5}-1)$
