Question

Two blocks of same mass m are connected to each other by spring of spring constant k. Initially spring is compressed by $x_0$ and blocks are connected by string. Whole system is placed on a smooth horizontal table. Now both blocks are given same horizontal velocity v perpendicular to spring and string is cut simultaneously. During subsequent motion of blocks.

Find the speed of blocks when spring is in its natural length position.

• A. $\sqrt{[v^2-\frac{k{x}_0^2}{2m}]}$
• B. $\sqrt{[v^2+\frac{k{x}_0^2}{2m}]}$
• C. $\sqrt{[v^2+\frac{k{x}_0^2}{4m}]}$
• D. $v$

Answer 1

The correct option is B

$\sqrt{[v^2+\frac{k{x}_0^2}{2m}]}$

At natural length

$2\times \frac{1}{2}m(v^2+v_1^2)$

$=2\times \frac{1}{2}m{v}^2+\frac{1}{2}k{x}_0^2$

$\sqrt{v^2+v_1^2}=\sqrt{[v^2+\frac{k{x}_0^2}{2m}]}$