At the surface of the moon, the acceleration due to the gravity of the moon is x. At a distance from the center of the moon equal to four times the radius of the moon, the acceleration due to the gravity of the moon is .

Gravity at a distance of 4R will be reduced to 1/16 th.

Explanation:

Given:

At the surface of the moon, the acceleration due to the gravity of the moon is x.

We have to find the gravity a t a distance of 4 times from the center of the moon.

Let the radius of the moon be "R".

And

The value of acceleration due to gravity is .

Formula:

⇒   ...where M is the mass of the moon.

Now

Gravity of the moon at the its surface:

⇒    ...equation (i)

Gravity of the moon at a distance of  :

⇒

⇒   ...equation (ii)

Dividing equation (i) with (ii) to find the relationship between the two.

⇒

⇒

⇒

⇒    ...as gm=x at the surface.

So,

We can say that the gravity at a distance of 4R will be reduced to 1/16 th.

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