A particle of mass $m = 1 \mathrm{kg}$ is dropped from a height $h = 40 \mathrm{cm}$ on a light horizontal platform fixed to one end of an elastic spring, the other being fixed to a base, as shown in the diagram. The particle collides with the platform and sticks to it. As a result, the spring is compressed by an amount $x = 10 \mathrm{cm}$. What is the force constant of the spring?
(Take $g = 10 \mathrm{m} {\mathrm{s}}^{-2}$)

• A

  $600 \mathrm{N} {\mathrm{m}}^{-1}$

   
• B

  $800 \mathrm{N} {\mathrm{m}}^{-1}$

   
• Correct answer
  C

  $1000 \mathrm{N} {\mathrm{m}}^{-1}$

   
• D

  $1200 \mathrm{N} {\mathrm{m}}^{-1}$

   

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