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

`g'=40\ m.s^(-2)`

Step-by-step 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*10^6\ m`

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

Now free fall acceleration on planet X:

`W=m.g'`

`20=0.5* g'`

`g'=40\ m.s^(-2)` irrespective of the height.

Answer 2

17.78 m/s^2

Step-by-step 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(R^(2))/((R+h)^(2))`

`g' = 40(\left (4* 10^6  \right )^(2))/((4+2)^(2)* 10^(12))`

g' = 17.78 m/s^2

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