The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

\frac{T}{4}

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\frac{T}{2}

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Solution

The correct option is C $\frac{T}{2}$
Let k be the force constant of spring. If k' is the force constant of each part, then k' = 4 k.
$∴$ Time period $= 2 π \sqrt{\frac{m}{4 k}} = \frac{1}{2} \times 2 π \sqrt{\frac{m}{k}} = \frac{T}{2}$ .
Hence, the correct answer is option (c).

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The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

The correct option is C T2Let k be the force constant of spring. If k' is the force constant of each part, then k' = 4 k. ∴ Time period =2π√m4k=12×2π√mk=T2. Hence, the correct answer is option (c).

The correct option is C $\frac{T}{2}$
Let k be the force constant of spring. If k' is the force constant of each part, then k' = 4 k.
$∴$ Time period $= 2 π \sqrt{\frac{m}{4 k}} = \frac{1}{2} \times 2 π \sqrt{\frac{m}{k}} = \frac{T}{2}$ .
Hence, the correct answer is option (c).