Q103 / 200 · NEET 2009 (Screening) · Physics

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

  • A
    $M g / k$
  • Correct answer
    B
    $2 \mathrm{Mg} / \mathrm{k}$
  • C
    $4 \mathrm{Mg} / \mathrm{k}$
  • D
    $M g / 2 k$

Solution

Key Idea Use the law of conservation of energy. Let $x$ be the extension in the spring. Applying conservation of energy $$ \begin{array}{ll} & \mathrm{mgx}-\frac{1}{2} \mathrm{kx}^2=0-0 \\ \Rightarrow \quad & \mathrm{x}=\frac{2 \mathrm{mg}}{\mathrm{k}} \end{array} $$

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

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