question_answer

A mass M, attached to a horizontal spring, executes S.H.M. with amplitude \[{{A}_{1}}\]. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude \[{{A}_{2}}\]. The ratio of\[\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)\]is                       [AIEEE 2011]

A)  \[{{\left( \frac{M+m}{M} \right)}^{1/2}}\]       

B)       \[\frac{M}{M+m}\]

C)  \[\frac{M+m}{M}\]      

D)       \[{{\left( \frac{M}{M+m} \right)}^{1/2}}\]

Correct Answer: A

Solution :

[a] At mean position, initial velocity

New velocity

or