Question

Two blocks $A$ ($5kg$) and $B$ ($2kg$) attached to the ends of a spring constant $1120N/m$ are on a smooth horizontal plane with the spring undefomed. Simultaneously velocities of $3m/s$ and $10m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$ then

• A. when the extension of the spring is maximum the velocities of $A$ and $B$ are zero.
• B. the maximum extension ofthe spring is $25$ $cm$.
• C. maximum extension and maximum compression occur alternately.
• D. the minimum speed of $B$ is $0$.

Answer 1

The correct option is B the maximum extension ofthe spring is $25$ $cm$.

Ans B

$\begin{array}{cc}{V}_{\text{com}}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}& =\frac{(5\times 3)+(2\times 10)}{5+2}\\ & w.r.t.=5m/s\end{array}$

$\begin{array}{c}\text{Mechanical energy conservation:}\\ Pi+K_i=P_f+K_f\\ 0+(\frac{1}{2}\times 5\times 2^2)=\frac{1}{2}k{x}^2+0\\ 10+25=\frac{1}{2}\times 1120x^2\\ \frac{70}{1120}=x^2\\ \frac{1}{4}m=x\\ 25cm=x\end{array}$