Question:
Time period of oscillation of mass \(m\) suspended from a spring is \(T\). What is the time period when the spring is cut in half and the same mass is suspended from one of the halves?
Time period of oscillation of mass \(m\) suspended from a spring is \(T\). What is the time period when the spring is cut in half and the same mass is suspended from one of the halves?
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Spring cut in half \(\Rightarrow\) stiffness doubles.
Updated On: Apr 16, 2026
- \( \frac{T}{2} \)
- \( \frac{T}{\sqrt{2}} \)
- \( \sqrt{2}T \)
- \( 2T \)
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The Correct Option is B
Solution and Explanation
Concept:
Time period of spring:
\[
T = 2\pi \sqrt{\frac{m}{k}}
\]
Step 1: Effect of cutting spring.
If spring is cut into half: \[ k' = 2k \]
Step 2: New time period.
\[ T' = 2\pi \sqrt{\frac{m}{2k}} = \frac{T}{\sqrt{2}} \]
Step 1: Effect of cutting spring.
If spring is cut into half: \[ k' = 2k \]
Step 2: New time period.
\[ T' = 2\pi \sqrt{\frac{m}{2k}} = \frac{T}{\sqrt{2}} \]
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