Question

Two blocks of masses $3\text{kg}$and $6\text{kg}$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200\text{N/m}$. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

• A. $30\text{cm}$
• B. $60\text{cm}$
• C. $15\text{cm}$
• D. $90\text{cm}$

Answer 1

The correct option is A $30\text{cm}$

Here reduced mass $\mu =\frac{6\times 3}{6+3}=2\text{kg}$

Initial kinetic energy of system w.r.t $CM$
$(K_i{)}_{\text{cm}}=\frac{1}{2}\frac{mM}{(m+M)}{V}_{rel}^2=(2-(-1){)}^2=9\text{J}$

At maximum extension $V_{rel}=0$

Final kinetic energy of system w.r.t $CM$
$(K_f{)}_{\text{cm}}=0$

Now, using WE theorem in COM frame
$K_i+U_i=K_f+U_t$
$\Rightarrow 9+0=0+\frac{1}{2}K{x}^2$
$\Rightarrow 9=100x^2$
$\Rightarrow x=0.3\text{m}=30\text{cm}$