A 1 ,kg block attached to a spring vibrates with a frequency of 1, Hz on a frictionless horizontal t

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13.Oscillations

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A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$

A

$0.25$

B

$0.35$

C

$0.5$

D

$2$

(JEE MAIN-2017)

Solution

Frequency of spring $(f)=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=1 \mathrm{Hz}$

$\Rightarrow 4 \pi^{2}=\frac{\mathrm{k}}{\mathrm{m}}$

If block of mass $\mathrm{m}=1 \mathrm{kg}$ is attached then, $k=4 \pi^{2}$

Now, identical springs are attached in parallel with mass

$\mathrm{m}=8 \mathrm{kg}$, Hence, $k_{e q}=2 k$

$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k} \times 2}{8}}=\frac{1}{2} \mathrm{Hz}$

Standard 11

Physics

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