A body of mass $64 \mathrm{~g}$ is made to oscillate turn by turn on two different springs A and B. Spring…

A body of mass $64 \mathrm{~g}$ is made to oscillate turn by turn on two different springs A and B. Spring $\mathrm{A}$ and $\mathrm{B}$ has force constant $4 \frac{\mathrm{N}}{\mathrm{m}}$ and $16 \frac{\mathrm{N}}{\mathrm{m}}$ respectively. If $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are period of oscillations of springs $\mathrm{A}$ and $\mathrm{B}$ respectively then $\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{\mathrm{~T}_{1}-\mathrm{T}_{2}}$ will be
  1. $1: 3$
  2. $3: 1$
  3. $1: 2$
  4. $2: 1$

Solution

$T=2 \pi \sqrt{\frac{m}{k}} \quad \therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{k_{2}}{k_{1}}}=\sqrt{\frac{16}{4}}=\frac{2}{1}$ $=\frac{T_{1}+T_{2}}{T_{1}-T_{2}}$ :

Asked in: MHT CET 2020 (19 Oct Shift 2)

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