Question

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 $(\frac{A_1}{A_2}$ is :-

• A. $(\frac{M}{M+m}{)}^{1/2}$
• B. $(\frac{M+m}{M}{)}^{3/2}$
• C. $\frac{M}{M+m}$
• D. $\frac{M+m}{M}$

Answer 1

The correct option is B $(\frac{M+m}{M}{)}^{3/2}$

$\begin{array}{c}{V}_1=A_1{W}_1\\ V_2=A_2{W}_2\\ M{V}_1=\left(M+m\right)V_2\\ \Rightarrow \frac{V_1}{V_2}=\frac{A_1{W}_1}{A_2{W}_2}=\left(\frac{M+m}{M}\right)\\ \Rightarrow \frac{A_1\sqrt{\frac{M}{K}}}{A_2\sqrt{\frac{M+m}{K}}}=\left(\frac{M+m}{M}\right)\\ \Rightarrow \frac{A_1}{A_2}={\left(\frac{M+m}{M}\right)}^{3/2}\end{array}$

Hence,

option $\left(B\right)$ is correct answer.