Question

In the situation shown in the figure the maximum possible compression in the spring is

• A. $v\sqrt{\frac{m}{k}}$
• B. $v\sqrt{\frac{2m}{k}}$
• C. $2v\sqrt{\frac{m}{k}}$
• D. $v\sqrt{\frac{m}{2k}}$

Answer 1

The correct option is D $v\sqrt{\frac{m}{2k}}$

$\begin{array}{c}\text{Maximum compression comes when both}\\ \text{the etjects move with same speed.}\\ \text{Since there is no external force, momentum}\\ \text{can be conserved:}\\ \begin{array}{c}mv=\left(2m\right)v^{\prime }\\ \Rightarrow v^{\prime }=\frac{v}{2}\end{array}\\ \text{Since, there is no friction energy}\\ \text{conserwation is also valid:}\\ \frac{1}{2}m{v}^2=\frac{1}{2}\left(2m\right){\left(\frac{v}{2}\right)}^2+\frac{1}{2}k(x{)}^2\end{array}$

$\begin{array}{c}\text{Where}x\text{is the maximum compression}\\ \begin{array}{cc}k{x}^2& =\frac{m{v}^2}{2}\\ \Rightarrow x& =v\sqrt{\frac{m}{2k}}\end{array}\\ \text{Option}D\text{is the correct option}\end{array}$