Question
Three mass and string system is in equilibrium. When $700\,gm$ mass is removed, then the system oscillates with a period of $3\,seconds$ . When the $500\,gm$ mass is also removed, then what will be new time period for system ..... $\sec$
✓
Answer
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}} \Rightarrow \mathrm{T} \propto \sqrt{\mathrm{m}}$
$\therefore \frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=\sqrt{\frac{\mathrm{m}_{2}}{\mathrm{m}_{1}}}=\sqrt{\frac{400}{900}}$
$\Rightarrow \frac{\mathrm{T}_{2}}{3}=\frac{2}{3} \Rightarrow \mathrm{T}_{2}=2 \mathrm{s}$
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