Question

On the moon’s surface, the acceleration due to gravity is 1.67 ms-2. If the radius of the moon is 1.74 × 106 m, calculate the mass of the moon.

Answer 1

Answer:

g=1.67m/s^2, R=1.74×10^6m, Mm= mass of moon

g=GMm/R^2

Mm=g/G×R^2

1.67×(1.75×10^6)^2/6.67×10^-11=7.4×10^22

mass of moon=7.4×10^22kg

Explanation:

Answer 2

Given:

Acceleration due to gravity on the surface of moon = 1.67 m$s^{-2}$

The radius of moon = 1.74 x $10^{6}$ m

To find:

The mass of the moon.

Solution:

To find the mass of the moon we will use the formula of acceleration due to gravity.

g = $\frac{GM}{R^2}$

where

g = acceleration due to gravity

G = universal gravitation constant = 6.673 x $10^{-11} Nm^2Kg^2$

M = mass of the object

R = radius of the object

Here it is given that

g = 1.67 m$s^{-2}$

R = 1.74 x $10^{6}$ m

Putting these values in the formula

1.67 = ( 6.67 x $10^{-11}$ x M) / (3.02 x $10^{12}$)

1.67 = 0.2218 x $10^{-23}$ M

M = 7.529 x $10^{23}$ Kg

Therefore the mass of the moon is  7.529 x $10^{23}$ Kg.