Question

The diagram shows three blocks and two springs. A massless rigid rod has connected the "end blocks”. Now, the middle block is given a velocity v. The maximum deformation of the spring is [mass of A=2M, mass of B=M, mass of C=M. Horizontal surface is smooth]

• A. $\sqrt{\frac{3M{v}^2}{5k}}$
• B. $\sqrt{\frac{3M{v}^2}{8k}}$
• C. $\sqrt{\frac{M{v}^2}{8k}}$
• D. $\sqrt{\frac{3M{v}^2}{4k}}$

Answer 1

The correct option is B $\sqrt{\frac{3M{v}^2}{8k}}$

At the time of maximum deformation in the springs all the three blocks would be moving with same velocity.
Let this velocity is $v_1.$ From momentum conservation
$mv=4m{v}_1\Rightarrow v_1=\frac{v}{4}$

Let $x$ is the deformation in both the springs then from work energy theorem.

$4m\times \frac{v_1^2}{2}-\frac{m{v}^2}{2}=-[\frac{k{x}^2}{2}\times 2-0]\Rightarrow x=\sqrt{\frac{3}{8}\frac{M{v}^2}{k}}$