Question

A block $m_1$ of mass $2.0\text{kg}$ is moving on a frictionless horizontal surface with a velocity of $1.0\text{m/s}$ towards another block $m_2$ of equal mass kept at rest as shown. The spring constant of the spring fixed at one end of $m_2$ is $100\text{N/m}$. The maximum compression of the spring is

• A. $2\text{cm}$
• B. $5\text{cm}$
• C. $10\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is C $10\text{cm}$

At the time of maximum compression velocities of both the blocks will be same (say $V$)

By conservation of linear momentum,
$2\times 1=4V$
$\Rightarrow V=0.5m/s$
By conservation of energy,
$\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}(m_1+m_2)(V{)}^2+\frac{1}{2}k{x}^2$
$\frac{1}{2}\times 2\times 1^2=\frac{1}{2}\times 4\times (0.5{)}^2+\frac{1}{2}\times 100\times x^2\Rightarrow x=0.1\text{m}=10\text{cm}$
$\therefore \left(c\right)$