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A mass 'm1m 1 ​ ' connected to a hori...

A mass 'm_1m 1 ​ ' connected to a horizontal spring performs S.H.M. with amplitude 'A'. While mass 'm_1m 1 ​ ' is passing through mean position another mass 'm_2m 2 ​ ' is placed on it so that both the masses move together with amplitude 'A_1A 1 ​ '. The ratio of \dfrac{A_1}{A} A A 1 ​ ​ is (m_2 < m_1)(m 2 ​

A

`[(m)/(m_(1)+m_(2))]^((1)/(2))`

B

`[(m_(1)+m_(2))/(m)]^((1)/(2))`

C

`[(m_(1))/(m_(1)+m_(2))]^((1)/(2))`

D

`[(m_(1)+m_(2))/(m_(2))]^((1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
`E_(1)=E_(2)`
`(1)/(2)m_(1)omega^(2)A^(2)=(1)/(2)(m_(1)+m_(2))omega^(2)A^(2)1`
`((A_(1))/(A))^(2)=(m_(1))/(m_(1)+m_(2))`
`(A_(1))/(A)=((m_(1))/(m_(1)+m_(2)))^(1//2)`
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