Two masses m₁ = 2,kg and m₂ = 5,kg are moving on a frictionless surface with velocities 10,m/s a

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5.Work, Energy, Power and Collision

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Two masses $m_1 = 2\,kg$ and $m_2 = 5\,kg$ are moving on a frictionless surface with velocities $10\,m/s$ and $3\,m/s$ respectively. An ideal spring is attached on the back of $m_2$ . The maximum compression of the spring will be ............... $\mathrm{m}$

A

$0.51$

B

$0.062$

C

$0.25$

D

$0.72$

Solution

At the time of maximum compression, both masses will have same velocities $\mathrm{v}_{\mathrm{o'}}$

from law of conservation of linear momentum.

$2 \times 10+5 \times 3=(2+5) v_{0}$

$35=7 v_{0} \Rightarrow v_{0}=5 \mathrm{m} / \mathrm{s}$

From $1 \mathrm{aw}$ of conservation of energy

$=\frac{1}{2} 2 \times 10^{2}+\frac{1}{2} 5 \times 3^{2}$

$=\frac{1}{2}(7) 5^{2}+\frac{1}{2}(1120) \mathrm{x}^{2}$

$=200+45=175+1120 \mathrm{x}^{2}$

$x=0.25 \mathrm{m}$

Standard 11

Physics

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