Two small bodies of mass of $2\, kg$ each attached to each other using a thread of length $10\, cm$, hang on a spring whose force constant is $200\, N/m$, as shown in the figure. We burn the thread. What is the distance between the two bodies when the top body first arrives at its highest position .... $cm$ ? (Take $\pi^2 = 10$)
Diffcult
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Time to move at upper extreme
$=\frac{T}{2}=\frac{\pi}{\omega}=\pi \sqrt{\frac{m}{k}}=\frac{\pi}{10} \mathrm{sec}$
Distance moved by lower block
$=\frac{1}{2} g t^{2}=\frac{1}{2} \times 10 \times \frac{\pi^{2}}{100}=50 \mathrm{cm}$
Seperation between the blocks $(20+10+50) \mathrm{cm}$ $=80 \mathrm{cm}$
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