Question

A man walks on the moon with a mass of 90 kilos and weighs 146 newtons. The radius of the moon is (1.74 x 10^6) meters. What is the mass of the moon?

a) 6.61 x 10^22 kilograms
b) 1.23 x 10^23 kilograms
c) 7.36 x 10^22 kilograms
d) 8.19 x 10^23 kilograms

Answer 1

By using the gravitational force equation, the mass of the moon is calculated to be 7.36 × 10^22 kg, making option c) the correct answer.

Step-by-step explanation:

To calculate the mass of the moon, we can use the equation for the gravitational force: F = G * (m1 * m2) / r^2, where F is the force of gravity (weight on the moon), G is the gravitational constant (6.674 × 10^-11 N × m^2/kg^2), m1 is the mass of the object (the man's mass), m2 is the mass of the moon, and r is the radius of the moon.

First, let's isolate the mass of the moon (m2) in the equation:

m2 = F * r^2 / (G * m1)

Plugging in the values given:

m2 = 146 N * (1.74 × 10^6 m)^2 / (6.674 × 10^-11 N × m^2/kg^2 * 90 kg)

Calculating this will give you the mass of the moon:

m2 = 7.36 × 10^22 kg

Therefore, the correct answer is c) 7.36 × 10^22 kilograms.