A mass M, attached to a horizontal spring, executes SHM with amplitude $A_{1}$ . When the mass M passes through its means position then a smaller mass m is placed over it and both of them move together with amplitude $A_{2}$ . The ratio of $(\frac{A_{1}}{A_{2}})$ is

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$\frac{M + m}{M}$

${(\frac{M}{M + m})}^{1 / 2}$

${(\frac{M + m}{M})}^{1 / 2}$

$\frac{M}{M + m}$

answer is C.

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Detailed Solution

Momentum is conserved

$\begin{array}{l} M A_{1} ω = (M + m) A_{2}^{} ω^{1} \\ M A_{1} \sqrt{\frac{k}{M}} = (M + m) A_{2}^{} \sqrt{\frac{k}{M + m}} \\ \frac{A_{1}}{A_{2}} = \frac{\sqrt{M + m}}{\sqrt{M}} \end{array}$

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