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13.Oscillations
medium
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
A
$A \sqrt{\frac{M-m}{M}}$
B
$A \sqrt{\frac{M}{M+m}}$
C
$A \sqrt{\frac{M+m}{M}}$
D
$A \sqrt{\frac{M}{M-m}}$
(JEE MAIN-2021)
Solution
Momentum of system remains conserved.
$p_{i}=p_{i}$
$MA \omega=( m + M ) A ^{\prime} \omega^{\prime}$
$M A \sqrt{\frac{k}{M}}=(m+M) A^{\prime} \sqrt{\frac{k}{m+M}}$
$A ^{\prime}= A \sqrt{\frac{ M }{ M + m }}$
Standard 11
Physics
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