Two blocks A and B of masses m and 2 m respectively, attached at opposite ends of a spring of constant K ,…

Two blocks $\mathrm{A}$ 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 $2{\mathrm{V}}_0$ and B given velocity ${\mathrm{V}}_0$ as shown.



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

1. $\frac{\mathrm{}l}{3}+\sqrt{\frac{8m{\mathrm{V}}_0^2}{3K}}$
2. $\frac{\mathrm{}l}{3}+\sqrt{\frac{2m{\mathrm{V}}_0^2}{3K}}$
3. $\frac{2l}{3}+\sqrt{\frac{2m{\mathrm{V}}_0^2}{3K}}$
4. $\frac{2l}{3}+\sqrt{\frac{8m{\mathrm{V}}_0^2}{3K}}$

Solution

$l_1=\frac{2ml}{2m+m}=\frac{2l}{3}$

$K_1{\mathit{\text{l}}}_1=Kl\Rightarrow K_1\left(\frac{2l}{3}\right)=Kl\Rightarrow K_1=\frac{3K}{2}$

$\left|x_{1\mathrm{ }\mathrm{m}\mathrm{a}\mathrm{x}}\right|=\sqrt{\frac{m{\left(2{\mathrm{V}}_0\right)}^2}{\frac{3K}{2}}}=\sqrt{\frac{8m{\mathrm{V}}_0^2}{3K}}$

$\left|d_{1\mathrm{ }\mathrm{m}\mathrm{a}\mathrm{x}}\right|=l_1+x_{1\mathrm{ }\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{2l}{3}+\sqrt{\frac{8m{\mathrm{V}}_0^2}{3K}}$

Asked in: Practice

Practice more Center of Mass Momentum and Collision questions on Aicharya