Question

A vertical spring oscillates with period 6 second with mass $m$ is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, $g = \pi^2 = 10 \text{ m/s}^2$ )

• A. 10 m
• B. 3 m
• C. 6 m
• D. 9 m

Hint:

For a mass on a spring, the static extension $x$ relates to the period by $T = 2\pi\sqrt{x/g}$.

Answer 1

The Correct Option is D

Step 1: Concept
Time period $T = 2\pi\sqrt{m/k}$. At rest, the weight $mg$ is balanced by spring force $kx$, so $mg = kx \implies m/k = x/g$.

Step 2: Meaning
Substituting $m/k$ in the period formula: $T = 2\pi\sqrt{x/g}$.

Step 3: Analysis
$6 = 2\pi\sqrt{x/\pi^2} = 2\pi(\sqrt{x}/\pi) = 2\sqrt{x}$. $3 = \sqrt{x}$.

Step 4: Conclusion
$x = 9 \text{ m}$. Final Answer: (D)