Originally Posted by

**gtbiyb** Hello this is a question from A2 level mechanics, am struggling to get the book answer. Here goes:

A bead, of mass *m* is threaded onto a smooth circular ring, of radius *r*, which is fixed in a vertical plane. The bead is moving on the wire so that its speed at the lowest point of its path is four times its speed, *v*, at the highest point.

Find *v* in terms of *r* and *g*.

My answer:

The usual technique is to work in terms of energy thus,

Loss in kinetic energy = gain in potential

1/2mv^2 - 1/2m(v/4)^2 = mgr

1/2m(v^2 - (v^2)/16) = mgr

(15/16)v^2 = 2gr

v^2 = 32gr/15

v = root(32gr/15)

But the book answer is v = root(4gr/15)

Any help offered is greatly appreciated.