MC Question!
An astronaut standing on the surface of the moon (mass = M, radius = R) holds a feather (mass = m) in one hand and a hammer (mass = 100m) in the other hand, both at the same height above the surface. If he releases them simultaneously, what is the acceleration of the hammer?
A. GM/R
B. GM/R^2
C. GMm/R^2
D. 1000 GM/R^2
E. 1000 GMm/R^2

Question

MC Question!
An astronaut standing on the surface of the moon (mass = M, radius = R) holds a feather (mass = m) in one hand and a hammer (mass = 100m) in the other hand, both at the same height above the surface. If he releases them simultaneously, what is the acceleration of the hammer?
A. GM/R
B. GM/R^2
C. GMm/R^2
D. 1000 GM/R^2
E. 1000 GMm/R^2

anonymous · Answer

The answer is indeed B. The weight of an object of mass in a gravitational field is given by F=ma (Newton's 2nd law). The gravitational force between two masses separated by a distance r is given by F=GMm/r^2. Equate the two F's, ma=GMm/r^2 and cancel the m's. The acceleration, a, comes out to be GM/R^2, thus answering the Question.

anonymous · Answer

$$ma=\frac{ GMm }{r ^{2} }$$

$$a=\frac{ GM }{ ^{r2} }$$

anonymous · Answer

Ohh, I understand now. Thank you for clearing this up!

anonymous · Answer

No problem, Newton's 2nd law is your friend!

anonymous · Answer

Oh,  one more question. How come we don't use the 100m that we got? It says the acceleration of the hammer, so isn't that the mass we should use?