Question

Two block of mass $3kg$ and $6kg$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200N/m$. Initially the spring is unstreatched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be:

• A. $30cm$
• B. $25cm$
• C. $20cm$
• D. $15cm$

Answer 1

The correct option is A $30cm$

By conserving linear momentum,

$\Rightarrow -3\times 1+6\times 2=6V-3V$

or, $9=9V$

or, $V=1$

$W_{dome}=\Delta K_E$

$W_{dome}=\frac{1}{2}\times 3(1{)}^2+\frac{1}{2}\times 6(2{)}^2-\frac{1}{2}\times (3{)}^2$

$\Rightarrow \frac{1}{2}\left(\overline{k}{x}^2\right)=\frac{1}{2}[3+24-9]$

$\Rightarrow 200\times x=18$

$\Rightarrow x=0.3m=30cm$