Question

An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force
on the object after it has been moved to a distance of 4R from the center of the planet?
(A) 16W (B) 4W (C)1/4W (D) 1/16 W

Answer 1

Weight on the surface,

$\displaystyle\longrightarrow\sf{W=-\dfrac {GMm}{R^2}}$

where M and m are masses of the planet and the object respectively. Negative sign shows that both are acting on the same direction.

After displacement, the weight will be, (M and m remain unchanged)

$\displaystyle\longrightarrow\sf{W'=-\dfrac {GMm}{(4R)^2}}$

$\displaystyle\longrightarrow\sf{W'=-\dfrac {GMm}{16R^2}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {W'=\dfrac {1}{16}W}}}$