A 2, Kg block moving with 10, m/s strikes a spring of constant π ^2 N/m attached to 2, Kg block at

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13.Oscillations

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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 ... $\sec$

A

$\sqrt{2}$

B

$\frac{1}{\sqrt{2}} $

C

$1 $

D

$\frac{1}{2}$

Solution

$m_{1}$ 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.

Standard 11

Physics

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