Q151 / 170 · Manipal (MET) 2021 · Physics

A mass $M$ is attached to a string, oscillates with a period of 2 s . If the mass is increased by 4 kg . The time period increases by 1 s . Assuming, that Hooke's law is obeyed, the initial mass $M$ was :

  • Correct answer
    A
    3.2 kg
  • B
    1 kg
  • C
    2 kg
  • D
    8 kg

Solution

$T=2=2 \pi \sqrt{\frac{M}{k}}$ and $2+1=2 \pi \sqrt{\frac{M+4}{k}}$ or $3=2 \pi \sqrt{\frac{M+4}{k}}$ $\therefore \quad \frac{4}{9}=\frac{M}{M+4}$ or $4 M+16=9 M$ or $M=\frac{16}{5}=3.2 \mathrm{~kg}$

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

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