Question

2) A body weighs W newton on the
surface of the earth. Its weight at a
height equal to half the radius of
earth will be​

Answer 1

Given,

$W=\dfrac {GMm}{R^2}$

We have to find $\dfrac {GMm}{\left (R+\dfrac {R}{2}\right)^2}.$

Well,

$\dfrac {GMm}{\left (R+\dfrac {R}{2}\right)^2}\\\\\\=\dfrac {GMm}{\left (\dfrac {3R}{2}\right)^2}\\\\\\=\dfrac{GMm}{\left (\dfrac {9R^2}{4}\right)}\\\\\\=\dfrac {4GMm}{9R^2}\\\\\\=\dfrac {4}{9}\cdot\dfrac {GMm}{R^2}\\\\\\=\mathbf {\dfrac {4}{9}W}$