Two identical particles each of mass $0.5 k g$ are interconnected by a light spring of stiffness $100 N / m,$ time period of small oscillation is

\frac{π}{5 \sqrt{2}} s

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\frac{π}{10 \sqrt{2}} s

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\frac{π}{5} s

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\frac{π}{10} s

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Solution

The correct option is D $\frac{π}{10} s$
We know $:$
$μ = \frac{m_{1} m_{2}}{m_{1} + m_{2}} = \frac{m}{2}$
Now $,$ $T = 2 π \sqrt{\frac{μ}{k}}$
$T = 2 π \sqrt{\frac{0.5}{2 \times 100}}$
$= \frac{2 π}{20}$
$= \frac{π}{10} s$
Hence,
option $(D)$ is correct answer..

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Two identical particles each of mass 0.5 kg are interconnected by a light spring of stiffness 100 N/m, time period of small oscillation is

The correct option is D π10sWe know: μ=m1m2m1+m2=m2Now, T=2π√μkT=2π√0.52×100=2π20=π10sHence,option (D) is correct answer..

Two identical particles each of mass $0.5 k g$ are interconnected by a light spring of stiffness $100 N / m,$ time period of small oscillation is

The correct option is D $\frac{π}{10} s$
We know $:$
$μ = \frac{m_{1} m_{2}}{m_{1} + m_{2}} = \frac{m}{2}$
Now $,$ $T = 2 π \sqrt{\frac{μ}{k}}$
$T = 2 π \sqrt{\frac{0.5}{2 \times 100}}$
$= \frac{2 π}{20}$
$= \frac{π}{10} s$
Hence,
option $(D)$ is correct answer..