Q131 / 180 · KCET 2014 · Physics

A \( 10 \mathrm{~kg} \) metal block is attached to a spring of spring constant \( 1000 \mathrm{~N} \mathrm{~m}^{-1} \), A block is
displaced from equilibrium position by \( 10 \mathrm{~cm} \) and released. The maximum acceleration of the
block is

  • Correct answer
    A
    \( 10 \mathrm{~ms}^{-2} \)
  • B
    \( 100 \mathrm{~ms}^{-2} \)
  • C
    \( 200 \mathrm{~ms}^{-2} \)
  • D
    \( 0.1 \mathrm{~ms}^{-2} \)

Solution

Given, mass, $\mathrm{m}=10 \mathrm{~kg}$; spring constant $k=1000 \mathrm{Nm}^{-1}$, displacement $x=10 \mathrm{~cm}=10 \times 10^{-2} \mathrm{~m}$ We know $\mathrm{F}=\mathrm{kx}$ Also, $\mathrm{F}=\mathrm{ma}$ $\Rightarrow \mathrm{kx}=\mathrm{ma}$ $\Rightarrow a=\frac{k x}{\mathrm{~m}}=\frac{1000 \times 10 \times 10^{-2}}{10}=10 \mathrm{~ms}^{-2}$ Therefore, maximum acceleration of the block is $10 \mathrm{~ms}^{-2}$

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

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