In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k$. The mass oscillates on a frictionless surface with time period $T$ and amplitude $A$. When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be
JEE MAIN 2021, Medium
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Momentum of system remains conserved.
$p_{i}=p_{i}$
$MA \omega=( m + M ) A ^{\prime} \omega^{\prime}$
$M A \sqrt{\frac{k}{M}}=(m+M) A^{\prime} \sqrt{\frac{k}{m+M}}$
$A ^{\prime}= A \sqrt{\frac{ M }{ M + m }}$
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