Passage II) Two identicla blocks P and Q have masses m each. They are attached to two identical springs initially unstretched. Now the left spring (along with P) is compressed by `A/2` and the right spring (along with Q) is compressed by A. Both the blocks are released simultaneously. They collide perfectly inelastically. Initially time period of both blocks was T.

The amplitude of combined mass is

Options

A. `(A)/(4)`
B. `(A)/(2)`
C. `(2A)/(3)`
D. `(3A)/(4)`

Answer

A

Explanation

From conservation of linear momentum
`-m(omegaA)/(2) +m omegaA =2 mv rArr v = (omegaA)/(4) = omega' A'`
`rArr (omegaA)/(4) = omega A' rArr A' = (A)/(4)`