Question

Two identical block 'P' and 'Q' each of mass 2 kg are placed on a smooth horizontal surface as shown.Block 'Q' is connected a light spring of force constant 100 N/m.If block 'p' is given an initial velocity 4 m/s towards the block 'Q' the maximum compression in the spring will be

• A. 0.1 m
• B. 0.2 m
• C. 0.4 m
• D. 0.8 m

Answer 1

The correct option is C 0.4 m

max compression will occur when both has same velocity and equal to half of initial velocity

$\begin{array}{c}\Rightarrow \frac{1}{2}l{x}^2=\frac{1}{2}m{\left(4\right)}^2-\frac{1}{2}m{\left(2\right)}^2\times 2\\ \Rightarrow k{x}^2=16m-8m\\ \Rightarrow k{x}^2=8m\\ \Rightarrow x^2\frac{8m}{k}=\frac{8\times 2}{100}\\ \Rightarrow x=\frac{4}{10}=0.4m\\ Hence,\\ optionCiscorrectanswer.\end{array}$