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  • A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude . When this

A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude \mathrm{A_{1}}. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses  move together with amplitude \mathrm{A_{2}}.  If the ratio \mathrm{\frac{A_{1}}{A_{2}}} is \mathrm{\frac{\alpha }{\alpha -1}}, then the value of \alpha will be _______.

Option: 1

16


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

By energy conservation,

\mathrm{TE_{initial}=IE_{final}}

\mathrm{\frac{1}{2} m_{1} \omega^2 A_1^2=\frac{1}{2} m_{2} \omega^2 A_2^2}

\mathrm{\begin{aligned} &\mathrm{m}_1=0.9 \mathrm{~kg} \\ &\text{m}_2=0.9 \mathrm{~kg}+0.124 \mathrm{~kg} \\ &\text{m}_2=1.024 \mathrm{~kg} \end{aligned}}

\mathrm{\begin{aligned} &\frac{A_1}{A_2}=\sqrt{\frac{m_2}{m_1}}=\sqrt{\frac{1024}{900}} \\ &\frac{A_1}{A_2}=\frac{2^5}{30}=\frac{32}{30}=\frac{\alpha}{\alpha-1} \end{aligned}}

\mathrm{\begin{aligned} &\frac{16}{15}=\frac{\alpha}{\alpha-1} \\ &\alpha=16 \end{aligned}}

Posted by

Deependra Verma

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