Question

if a man weighs 60 kg on the surface of the earth the height above the surface of the Earth where is weight is 30 kg is
a)0.41R
b)√2R
c)R/√2
d)R/2​

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• Mass of man on surface of Earth= 60kg

• Mass of man on above the surface of Earth = 30kg

$\Large\underline{\underline{\sf To\:Find:}}$

• Height = ?

$\Large\underline{\underline{\sf Formula\:Used:}}$

$\large{\boxed{\boxed{\sf \pink{F=\dfrac{GMm}{R^2}}}}}$

$\Large\underline{\underline{\sf Solution:}}$

Let the height is h

Force is inversely proportional to Square of radius.

$\Large{\sf \red{F\:\:\:\alpha\:\:\:\dfrac{1}{R^2}}}$

⛬

$\implies{\sf \dfrac{F_1}{F_2}=\dfrac{(R+h)^2}{R^2}}$

$\implies{\sf \dfrac{60}{30}=\left(\dfrac{R+h}{R}\right)^2 }$

$\implies{\sf \sqrt{2}=\dfrac{R+h}{R}}$

$\implies{\sf R+h=\sqrt{2}R }$

$\implies{\sf h=\sqrt{2}R-R}}$

$\implies{\sf h=( \sqrt{2}-1)R }$

$\implies{\sf h=(1.41-1)R}$

$\implies{\sf \red{h=0.41R }}$

$\Large\underline{\underline{\sf Answer:}}$

Option (a) 0.41R

⛬ The height above the surface of the Earth where is weight is 30 kg is 0.41R

Answer 2

Explanation:

g'=g/2

g/2=g/(1+h/R)²

(1+h/R)²= 2

1+h/R=√2

h/R=√2-1

h/R=1.41-1=0.41

h=0.41R

Ans:(A) 0.41 R