At the surface of the Moon, the acceleration due to the gravity of the Moon is . At a distance from the center of the Moon equal to three times the radius of the Moon, the acceleration due to the gravity of the Moon is
A) 9 .
B) /3.
C) /4.
D) /9.
E) 27 .

Question

At the surface of the Moon, the acceleration due to the gravity of the Moon is  . At a distance from the center of the Moon equal to three times the radius of the Moon, the acceleration due to the gravity of the Moon is
A) 9 . 
B) /3. 
C) /4. 
D) /9. 
E) 27 .

Quizplus · Accepted Answer

The acceleration due to the gravity of the Moon at a distance from the center of the Moon equal to three times the radius of the Moon can be found using the inverse square law of gravitational force. According to the law, the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

If we denote the radius of the Moon as r, then the distance from the center of the Moon to a point on its surface is 2r (since the radius of the Moon is r and the distance from the center to the surface is also r). Therefore, the distance from the center of the Moon to a point at a distance of 3r from the center is 4r.

Let's assume that the acceleration due to gravity at a distance of 3r from the center of the Moon is a. Then, we can write:

a = GM/(4r)^2

where G is the gravitational constant (6.674 x 10^-11 Nm^2/kg^2) and M is the mass of the Moon.

Now, we can substitute the given value of the acceleration due to gravity at the surface of the Moon (11.08 m/s^2) for a and simplify the equation to solve for a:

11.08 = GM/(4r)^2

GM = 11.08 x 16r^2

M = (11.08 x 16r^2)/G

Substituting this value of M in the equation for a, we get:

a = [G(11.08 x 16r^2)/G]/(4r)^2

a = 11.08/36

a = 0.307 m/s^2

Therefore, the acceleration due to the gravity of the Moon at a distance from the center of the Moon equal to three times the radius of the Moon is 0.307 m/s^2, which is equal to 11.08/36 or approximately 0.307 times the acceleration due to gravity at the surface of the Moon.

So, the best choice is D: 11eb1367_5146_41d1_8021_a7e817b0edd8_TB7291_11 /9.

At the Surface of the Moon, the Acceleration Due to the Gravity