Question

An object of mass 0.50 kg is transported to the surface of Planet X where the object’s weight is measured to be 20 N. The radius of the planet is 4.0 x 10^6 m. What free fall acceleration will the 0.50-kg object experience when transported to a distance of 2.0 x 10^6 m from the surface of this planet?

Answer 1

Answer:

$g'=40\ m.s^{-2}$

Explanation:

Given:

• mass of the object, $m=0.5\ kg$

• weight of the object on planet x, $W=20\ N$

• radius of the planet, $R=4\times10^6\ m$

• radial distance between the planet and the object, $r=2\times 10^6\ m$

Now free fall acceleration on planet X:

$W=m.g'$

$20=0.5\times g'$

$g'=40\ m.s^{-2}$ irrespective of the height.

Answer 2

Answer:

17.78 m/s^2

Explanation:

m = 0.5 kg

Weight on the planet, W = 20 N

Acceleration due to gravity on the surface of planet, g = W / m

g = 20 / 0.5 = 40 m/s^2

Radius of planet, r = 4 x 10^6 m

height, h = 2 x 10^6 m

Let the acceleration due to gravity at a height is g'.

According to the formula of acceleration due to gravity at height is

$g' = g\frac{R^{2}}{(R+h)^{2}}$

$g' = 40\frac{\left (4\times 10^6 \right )^{2}}{(4+2)^{2}\times 10^{12}}$

g' = 17.78 m/s^2

Thus, the acceleration due to gravity at height is  17.78 m/s^2 .