Two identical blocks `A` and `B` , each of mass `m` resting on smooth floor are connected by a light spring of natural length `L` and spring constant `k`, with the spring at its natural length. A third identical block `C` (mass `m`) moving with a speed `v` along the line joining `A` and `B` collides with `A`. The maximum compression in the spring is

Options

A. `vsqrt(m/(2k))`
B. `msqrt(v/(2k))`
C. `sqrt((mv)/(k))`
D. `(mv)/(2k)`

Answer

A

Explanation

Law of conservation of momentum –
mv = (m + m)v.
`implies v. =v/2`

Law of conservation of energy –
`(KE)_C=(KE)_("system")+(PE)_("system")`
`implies 1/2mv^2=1/2 (2m)(v.)^2+1/2kx^2`
`implies kx^2 =mv^2 -(mv^2)/2 =1/2mv^2`
`implies x = v sqrt(m/(2k))`