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## Homework Statement

[Edit: Copy of figure added by moderator]

[1]: http://i.stack.imgur.com/VGhTc.png

(sorry for the shabby figure!)

The problem-a bob of mass ##m## is hanging from a cart of mass ##M##. The system is released from rest from the position shown. Find the maximum speed of the cart relative to ground. String length is ##l##. The answer - ##v= \sqrt{\frac{m^2gl}{M(M+m)}}##

## Homework Equations

## The Attempt at a Solution

My try- the speed of the cart must be maximum when the bob is at the lowest point relative the the cart. As there is no external force along X-axis, the speed of COM along X axis must be constant. Now, wrt cart, the speed of bob at that point must be ##-\sqrt{gl}## towards left. So, wrt ground, it is ##(v-\sqrt{gl})## towards right, where ##v## is the velocity of cart at that instant relative to ground, which must be the maximum speed, as said earlier. Hence,

##v_{com}=\frac{Mv+m(v-\sqrt{gl})}{M+m}=0##(initially, it was at rest)

Which gives the answer as ##v=\frac{m\sqrt{gl}}{M+m}##.

I don't understand where I have gone wrong. Any help would be appreciated. Thanks in advance!!