Question

A new planet is discovered that has twice the Earth's mass and twice the Earth's radius. On the surface of this new planet a person who weights 500 N on Earth would experience a gravitational force of ______.

(A) 125 N
(B) 250 N
(C) 500 N
(D)) 1000 N
(E) 2000 N

Answer 1

Answer:

option B

Explanation:

Radius of new planet,R' = 2R

Mass of the earth, M' = 2 M

R and M is the Radius and Mass of the earth.

Weight of the person on earth = 500 N

Weight of the person in the new planet = ?

We know acceleration due to gravity is calculated by using formula

   $g = \dfrac{GM}{R^2}$

now, acceleration due to gravity on the new planet

   $g' = \dfrac{GM'}{R'^2}$

   $g' = \dfrac{G(2M)}{(2R)^2}$

   $g' =\dfrac{1}{2} \dfrac{GM}{R^2}$

   $g' =\dfrac{g}{2}$

here acceleration due to gravity is half in new planet, so weight will also be half on the new planet.

Weight on the new plane is equal to $\dfrac{500}{2}$ = 250 N

correct answer is option B