Question

Two identical masses each of mass $m$ are connected by a spring and placed on a smooth surface. A third identical mass moving with speed $v_0$ collides with one of the two masses perfectly inelastically. Choose the correct option.

• A. Centre of mass of the given blocks moves with a constant speed $\frac{v_0}{3}$ after collision
• B. Maximum elongation in spring is $\sqrt{\frac{m{v}_0^2}{6k}}$
• C. Maximum compression in spring is $\sqrt{\frac{m{v}_0^2}{2k}}$
• D. Maximum compression in spring is $\sqrt{\frac{m{v}_0^2}{6k}}$

Answer 1

The correct option is A Centre of mass of the given blocks moves with a constant speed $\frac{v_0}{3}$ after collision

Velocity of center of mass $=\frac{m{v}_0+m\times 0+m\times 0}{m+m+m}$

$=\frac{v_0}{3}.$

Maximum compression occur when all are move with same velocity by momentum conservation common velocity $v=\frac{v_0}{3}$

$\Rightarrow \frac{1}{2}{kx}^2=\frac{1}{2}{{mv}_0}^2-3\times \frac{1}{2}{\left(\frac{v_0}{3}\right)}^2\times m$

$\Rightarrow {kx}^2=\frac{1}{2}\frac{2}{3}{v_0}^2\times m$

$\Rightarrow x=\sqrt{\frac{m{v_0}^2}{3k}}$

Only option A correct.

Hence, the answer is option A.