A certain object has mass of 2.26 kg on the surface of Earth. If the radius of the Moon is 0.276 times the radius of Earth and the mass of the Moon is 0.0123 times the mass of Earth, the object's weight on the surface of the Moon is approximately
A) 2.26 kg.
B) 3.58 N.
C) 0.364 kg.
D) 22.2 N.
E) 9.81 N.

Question

Quizplus · Accepted Answer

On the surface of Earth, the weight (F) of the object can be found using the formula:

F = mg

where m is the mass of the object and g is the acceleration due to gravity on Earth. The value of g on Earth is approximately 9.81 m/s^2.

F = (2.26 kg)(9.81 m/s^2) = 22.2 N

To find the weight of the object on the surface of the Moon, we need to use the formula:

F = G(m1m2)/r^2

where G is the gravitational constant, m1 is the mass of the object, m2 is the mass of the Moon, and r is the distance between the center of the object and the center of the Moon.

We can simplify this formula by using the fact that the radius of the Moon is 0.276 times the radius of Earth:

r = (0.276)(6.37 × 10^6 m) = 1.76 × 10^6 m

We can also use the fact that the mass of the Moon is 0.0123 times the mass of Earth:

m2 = (0.0123)(5.97 × 10^24 kg) = 7.36 × 10^22 kg

Plugging these values into the formula, we get:

F = G(m1m2)/r^2 
F = (6.67 × 10^-11 N m^2/kg^2)(2.26 kg)(7.36 × 10^22 kg)/(1.76 × 10^6 m)^2 
F ≈ 3.58 N

Therefore, the object's weight on the surface of the Moon is approximately 3.58 N, which is answer choice B.

A Certain Object Has Mass of 2