Two identical balls, each of mass `m`, are tied with a string and kept on a frictionless surface. Initially, the string is slack. They are given velocities `2u` and `u`. in the same direction. Collision between the balls is perfectly elastic.

What is the final in kinetic energy of the balls?

Options

A. `"mu"^(2)//4`
B. `"mu"^(2)//2`
C. `3"mu"^(2)//4`
D. none of these

Answer

A

Explanation

After the first collision the velocities are as shown in figure.

Now after some time the string will become tight. Let at that point the comon velocity of the balls be `v`.

`2mv+"mu"+2"mu"impliesv=3u/2`
`KE_(i)=1/2"mu"^(2)+1/2m(2u)^(2)=5"mu"^(2)//2`
`KE_(f)=1/2 2m v^(2)=1/22m((3u)//2)^(2)=(9"mu"^(2))/4`
`KE_(Loss)=KE_(i)-KE_(f)=(5"mu"^(2))/2(9"mu"^(2))/4="mu"^(2)//4`