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A horizontal spring -block system of mas...

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 on it the two move together The new amplitude of vibration is `(A` being its initial amplitude)

A

`sqrt((2)/(3))A`

B

`sqrt((3)/(2))A`

C

`sqrt(2)A`

D

`(A)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Conserving momentum `: 2V=3V'`
`rArr V'=(2)/(3)V`.
`E_(i)=(1)/(2)m_(1)V_(1)^(2)=(1)/(2).2V^(2)=V^(2)`
`rArr (1)/(2) KA^(2)=V^(2)`.
`E_(f)=(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)/(3)E_(i)`
` ( :' E_(i)=V^(2)` from above `)`
`rArr (1)/(2)KA^('2)=(2)/(3)((1)/(2)KA^(2))`
`rArr A'=sqrt((2)/(3))A` Ans.
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