Question

Two blocks of mass 3 kg and 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant k=200Nm−1k=200Nm−1 are imparted in opposite directions to the respective blocks as shown in figure. The maximum extension of the spring will be

• A. $15cm$
• B. $20cm$
• C. $25cm$
• D. $30cm$

Answer 1

The correct option is D $30cm$

At maximum extension velocity of both the block will be same .

Let $v$ be the common velocity of the blocks (towards right)

From conservation of linear momentum.

$\begin{array}{c}\left(3+6\right)v=6\times 2-3\times 1=9\\ orv=1m/s\end{array}$

now let $x$ be the maximum extension in the spring.

from conservation of mechanical energy

$\begin{array}{c}\frac{1}{2}\times \left(3\right){\left(1\right)}^2+\frac{1}{2}\times \left(6\right){\left(2\right)}^2=2\left(200\right)x^2+\frac{1}{2}\times \left(9\right){\left(1\right)}^2\\ or3+24=200x^2+9\\ orx=\sqrt{\frac{18}{200}}\\ orx=0.3m\\ x=30cm\end{array}$

Hence,

Option $D$ is correct.