A horizontal spring `-` block system of mass `2kg` executes `S.H.M.` . When the block is passing through its equilibrium position, an object of mass `1kg` is put gently on it and the two move together. The new amplitude of vibration is `(A` being is initial amplitude `) :`

Options

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

Answer

A

Explanation

Conserving momentum `:2V=3V'rArr V'=2/3 V`
`E_(1)=1/2 m_(1)V_(1)^(2) =1/(2).2.V^(2)=V^(2) rArr 1/2 KA^(2) =V^(2)`.
`E_(1)=1/2 m_(2)V_(2)^(2)=1/(2).3.(2)/(3).(2)/(3) V^(2)=2/3 V^(2) rArr 1/2 KA'^(2)=2/3 V^(2)=2/3E_(1) " " ` (` :' E_(1)=V^(2)` from above)
`rArr 1/2 KA'^(2) =2/3 (1/2KA^(2)) " " rArr A'=sqrt(2/3) A`