Question

Two blocks of masses $m_{1}=2kg$ and $m_{2}=5kg$ are moving in the same direction along a frictionless surface with speeds $10ms^{- 1}$ and $3ms^{- 1}$ respectively. An ideal spring with $K=1120Nm^{- 1}$ is attached to the back side of $m_{2}$ . Find the maximum compression of the spring when the blocks collide.

• A. $0.50m$
• B. $0.25m$
• C. $0.75m$
• D. $1m$

Answer 1

Answer: (B)

Using conservation of linear momentum
$m_{1}\times 10+m_{2}\times 3=\left(m_{1} + m_{2}\right)V_{CM}$
$2\times 10+5\times 3=7V_{cM}$
$V_{CM}=5ms^{- 1}$
At maximum compression of spring both particles will acquire common velocity $V_{CM}=5ms^{- 1}$
Energy conservation
$\Rightarrow \frac{1}{2}\times 2\times 10^{2}+\frac{1}{2}\times 5\times 3^{2}=\frac{1}{2}\times 7\times 5^{2}+\frac{1}{2}kx^{2}$
$\Rightarrow x=0.25m$