Question:
If the period of a oscillation of mass ' m ' suspended from a spring is $2\text{ s}$ , then the period of suspended mass ' 4 m ' with the same spring will be}
If the period of a oscillation of mass ' m ' suspended from a spring is $2\text{ s}$ , then the period of suspended mass ' 4 m ' with the same spring will be}
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If the mass becomes 4 times, the time period doubles because $\sqrt{4} = 2$.
Updated On: May 14, 2026
- 1 s
- 3 s
- 2 s
- 4 s
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The Correct Option is D
Solution and Explanation
Step 1: Concept
The time period of a mass-spring system is $T = 2\pi\sqrt{\frac{m}{k}}$.
Step 2: Meaning
The period is directly proportional to the square root of the mass ($T \propto \sqrt{m}$).
Step 3: Analysis
$\frac{T_2}{T_1} = \sqrt{\frac{m_2}{m_1}}$
$\frac{T_2}{2} = \sqrt{\frac{4m}{m}} = \sqrt{4} = 2$
$T_2 = 2 \times 2 = 4\text{ s}$.
Step 4: Conclusion
The new time period will be $4\text{ s}$. Final Answer: (D)
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