The time period of oscillation of a mass suspended by a spring (force constant k) is T. If the spring is cut into three equal pieces, the force constant of each part and the periodic time, if the same mass is suspended from one piece are

$k, \frac{T}{3}$

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$3 k, T$

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$3 k, \sqrt{3} T$

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$3 k, \frac{T}{3}$

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Solution

The correct option is D
$3 k, \frac{T}{3}$

$k_{1} l_{1} = k l =$ constant $\Rightarrow k_{1} (\frac{1}{3}) = k l \Rightarrow k_{1} = 3 k$

$\Rightarrow T = 2 π \sqrt{\frac{m}{k_{1}}} = 2 π \sqrt{\frac{m}{3 k}} = \frac{T}{\sqrt{3}}$

Hence the correct option is $3 k, \frac{T}{\sqrt{3}}$

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The time period of oscillation of a mass suspended by a spring (force constant k) is T. If the spring is cut into three equal pieces, the force constant of each part and the periodic time, if the same mass is suspended from one piece are

The correct option is D 3k,T3 k1l1=kl= constant ⇒k1(13)=kl⇒k1=3k ⇒T=2π√mk1=2π√m3k=T√3 Hence the correct option is 3k,T√3

The correct option is D
$3 k, \frac{T}{3}$

$k_{1} l_{1} = k l =$ constant $\Rightarrow k_{1} (\frac{1}{3}) = k l \Rightarrow k_{1} = 3 k$

$\Rightarrow T = 2 π \sqrt{\frac{m}{k_{1}}} = 2 π \sqrt{\frac{m}{3 k}} = \frac{T}{\sqrt{3}}$

Hence the correct option is $3 k, \frac{T}{\sqrt{3}}$