Question

Three masses $700gm$, $500gm$, $400gm$ are suspended at the end of springs and in equilibrium. When $700gm$ mass is removed, the system oscillates with a period of $3$ seconds, when $500gm$ is also removed, it will now oscillate with

• A. $1sec$
• B. $2sec$
• C. $3sec$
• D. $\sqrt{\frac{12}{5}}sec$

Answer 1

Answer: (B)

$2sec$

$\begin{array}{c}\text{we know that Time periad of spring oscillation-}\\ T=2\pi \sqrt{\frac{m}{k}}\text{where}\begin{array}{cc}m& =\text{Total mass}\\ k& =\text{spring const.}\end{array}\end{array}$

$\begin{array}{c}\text{when}700gm\text{mass is removed}\\ m_{\text{left}}=900gm\\ \Rightarrow T=2\pi \sqrt{\frac{900}{K}}=3sec\\ \Rightarrow \frac{2\pi }{\sqrt{K}}=\frac{1}{10}\text{units}\end{array}$

$\begin{array}{c}\text{When}500gm\text{mass is also removed}\\ m\text{left}=400gm\\ \Rightarrow T=2\pi \sqrt{\frac{400}{k}}=20\times \frac{2\pi }{\sqrt{K}}=20\times \frac{1}{10}=2sec\\ \Rightarrow \text{Time period}=2sec.\end{array}$