A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor. The time for which rear moving block remain in contact with spring will be ... $\sec$
Diffcult
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$m_{1}$ stay in contact with spring for $T / 2$
$T=2 \pi \sqrt{\frac{\mu}{k}}$
where,
$\mu=\frac{m_{1} m_{2}}{m_{1}+m_{2}}=\frac{2 \times 2}{2+2}=1 k g$
$=2 \pi \sqrt{\frac{1}{\pi^{2}}} \quad k=\pi^{2}$
$T=2 \sec$
Time for moving block remain in contact with
spring will be $\frac{T}{2} \Rightarrow \frac{2}{2}=1$ sec.
hence $t=\frac{T}{2}$ is $1$ sec.
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