Solving GRE Spheres: Find h0 from h

[Pupil]

"Two small spheres of putty, A and B, of mass M and 3M, respectively, hang from the ceiling on strings of equal length l. Sphere A is drawn aside so that it is raised to a height h₀ and then released. Sphere A collides with sphere B; they stick together and swing to a maximum height h equal to "

This is an exercise I am perplexed about as to why I got the wrong answer. I used conservation of energy.

Ei = mgh₀

Ef = (m+3m)gh

Ef = Ei

mgh₀ = (m+3m)gh

Therefore h = (1/4)m

This answer is wrong. The correct answer is (1/16)h₀. Where'd I go wrong? Thanks!

 

[hamster143]

They stick together after collision, that (as well as the fact that they are made of putty) should tell you that collision is inelastic and kinetic energy is not conserved. You have to consider momentum conservation to calculate Ef.

 

[Pupil]

Thanks!