Question

Two blocks 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 unstretched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be

• A. $57cm$
• B. $25cm$
• C. $30cm$
• D. $15cm$

Answer 1

The correct option is C $30cm$

From conservation of momentum

Initial momentum = momentum of center of mass

$m_1{u}_1+m_2{u}_2=(m_1+m_2)V_{cm}$

$6\times 2-3\times 1=(6+3)V_{cm}$

$V_{cm}=1m{s}^{-1}$

From conservation of energy.

$\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2=\frac{1}{2}k{x}^2+\frac{1}{2}(m_1+m_2)V_{cm}^2$

$\frac{1}{2}6\times 2^2+\frac{1}{2}3\times 1^2=\frac{1}{2}200\times x^2+\frac{1}{2}(6+3)\times 1^2$

$x=0.3m=30cm$

Hence, extension of spring is $30cm$