Question

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 _____.

Answer 1

Answer: The acceleration due to gravity on the surface of the moon is 1.620 m/s2. 2) The radius of the Earth is 6.38 x 106 m.

Answer 2

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

Step-by-step 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
`g_m` .

Formula:

⇒
`g_m=(GM)/(R^2)` ...where M is the mass of the moon.

Now

Gravity of the moon at the its surface:

⇒
`g_m=(GM)/(R^2)` ...equation (i)

Gravity of the moon at a distance of
`4R`:

⇒
`g_m_1=(GM)/((4R)^2)`

⇒
`g_m_1=(GM)/(16R^2)` ...equation (ii)

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

⇒
`(g_m_1)/(g_m) =(GM)/(16R^2)* (R^2)/(GM)`

⇒
`(g_m_1)/(g_m) =(1)/(16)`

⇒
`g_m_1 =g_m((1)/(16))`

⇒
`g_m_1 =x((1)/(16))` ...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.