JEE Mains · Physics · STD 11 - 13. oscillations
A mass \(m\) attached to free end of a spring executes SHM with a period of \(1\; s\). If the mass is increased by \(3\; kg\) the period of oscillation increases by one second, the value of mass \(m\) is \(..............kg\).
- A \(0.1\)
- B \(100\)
- C \(1\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(T =2 \pi \sqrt{\frac{ m }{ k }}=1\) \(T ^{\prime}=2 \pi \sqrt{\frac{ m +3}{ k }}=2\) \(\frac{ T }{ T ^{\prime}}=\sqrt{\frac{ m }{ m +3}}=\frac{1}{2}\) \(\Rightarrow \frac{ m }{ m +3}=\frac{1}{4}\) \(m =1\)
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