Q134 / 170 · Manipal (MET) 2020 · Physics

Time period of oscillation of mass $m$ suspended from a spring is $T$. What is the time period when the sppring is cut in half and the same mass is suspended from one of the halves?

  • A
    $T / 2$
  • Correct answer
    B
    $T / \sqrt{2}$
  • C
    $\sqrt{2} T$
  • D
    $2 T$

Solution

Time period of oscillation of mass $m$ suspended from a spring $T=2 \pi \sqrt{\frac{m}{k}}$ If the spring is cut into two halves, then the new time period. $T^{\prime}=2 \pi \sqrt{\frac{m}{2 k}}=2 \frac{\pi}{\sqrt{2}} \sqrt{\frac{m}{k}}=\frac{T}{\sqrt{2}}$

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

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