Question

Two blocks $A$ and B of masses $m$ and $2m$ respectively, attached at opposite ends of a spring of constant $K$ , placed on a smooth horizontal surface. Spring is initially at its natural length $l$ . A is given a velocity $2V_0$ and B given velocity $V_0$ as shown.



Maximum separation between $m$ and centre of mass of the system will be:

• A. $\frac{l}{3}+\sqrt{\frac{8m{V}_0^2}{3K}}$
• B. $\frac{l}{3}+\sqrt{\frac{2m{V}_0^2}{3K}}$
• C. $\frac{2l}{3}+\sqrt{\frac{2m{V}_0^2}{3K}}$
• D. $\frac{2l}{3}+\sqrt{\frac{8m{V}_0^2}{3K}}$

Answer 1

Answer: (D)

$l_1=\frac{2ml}{2m+m}=\frac{2l}{3}$
$K_1{\left(\text{l}\right)}_1=Kl\Rightarrow K_1\left(\frac{2l}{3}\right)=Kl\Rightarrow K_1=\frac{3K}{2}$
$\left|x_{1max}\right|=\sqrt{\frac{m{\left(2V_0\right)}^2}{\frac{3K}{2}}}=\sqrt{\frac{8m{V}_0^2}{3K}}$
$\left|d_{1max}\right|=l_1+x_{1max}=\frac{2l}{3}+\sqrt{\frac{8m{V}_0^2}{3K}}$