Calculate the magnitude of the acceleration due to gravity on the surface of earth due to the moon.

Explanation:

We know that the gravity on the surface of the moon is,

Gravity at a height h above the surface of the moon will be given as:

..........................(1)

where:

G = universal gravitational constant

m = mass of the moon

r = radius of moon

We have:

Now put the respective values in eq. (1)

is the gravity on the moon the earth-surface.

112.06 kg - Thats heavy !

Explanation:

Let's do force balance here. Let the object of our interest be George. The forces acting on him are the tension in  the upward direction, his weight in the downward direction and the centrifugal force in the downward direction. Considering the upward and downward directions on the y-axis and f=given the fact that George doesn't move up or down, the forces are balanced along the y-axis. Hence doing force balance:

magnitude of forces upward =magnitude of forces downward

i.e., Tension(T) = Weight(mg) + Centrifugal force (mv²/r)

where: 'm' is the mass of George, g is the acceleration due to gravity (9.8 m/s²). v is the speed with which George moves (14.1 m/s) and r is the radius of the circle in which he's moving at the instant (Here since he's swinging on the rope, he moves in a circle with radius as the length of the rope and hence r=7.3m).

therefore, T = m (9.8 + (14.1)²/7.3) = 4150 N

Therefore, m = 112.06 kg