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:

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 $g_m$ .

Formula:

⇒ $g_m=\frac{GM}{R^2}$   ...where M is the mass of the moon.

Now

Gravity of the moon at the its surface:

⇒ $g_m=\frac{GM}{R^2}$    ...equation (i)

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

⇒ $g_m_1=\frac{GM}{(4R)^2}$

⇒ $g_m_1=\frac{GM}{16R^2}$   ...equation (ii)

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

⇒ $\frac{g_m_1}{g_m} =\frac{GM}{16R^2}\times \frac{R^2}{GM}$

⇒ $\frac{g_m_1}{g_m} =\frac{1}{16}$

⇒ $g_m_1 =g_m(\frac{1}{16})$

⇒ $g_m_1 =x(\frac{1}{16})$    ...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.