The spring block system lies on a smooth horizontal surface. The free end of the spring is being pulled towards the right with constant speed ${\mathrm{V}}_0=2 \mathrm{m} {\mathrm{s}}^{-1}$. At $\mathrm{t}=0\mathrm{ }\mathrm{s}$, the spring of constant $\mathrm{k}=100\mathrm{ }\mathrm{N} \mathrm{c}{\mathrm{m}}^{-1}$ is unstretched and the block has a speed $1\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ to left. The maximum extension of the spring will be

• A

  $\mathrm{2 }\mathrm{c}\mathrm{m}$
• B

  $4\mathrm{ }\mathrm{c}\mathrm{m}$
• Correct answer
  C

  $6\mathrm{ }\mathrm{c}\mathrm{m}$
• D

  $8\mathrm{ }\mathrm{c}\mathrm{m}$

Solution

In the frame (inertial w.r.t. earth) of the free end of spring, the initial velocity of the block is $\mathrm{3 }\mathrm{m}/\mathrm{s}$ to left and the spring is unstretched.




Applying conservation of energy between initial and maximum extension state,

$\frac{1}{2}\mathrm{m}{\mathrm{V}}^2=\frac{1}{2}\mathrm{k}{\mathrm{A}}^2$

$\mathrm{A}=\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}\mathrm{ }\mathrm{V}=\sqrt{\frac{4}{10000}}\times 3=6\mathrm{ }\mathrm{c}\mathrm{m}$ 

Hence, the correct answer is option: 'C'.