JEE Mains · Physics · STD 11 - 13. oscillations
A block of mass \(0.1\, kg\) is connected to an elastic spring of spring constant \(640\, Nm^{-1}\) and oscillates in a damping medium of damping constant \(10^{-2}\, kg\,s^{-1}\) . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... \(s\)
- A \(2\)
- B \(3.5\)
- C \(5\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(3.5\)
Step-by-step Solution
Detailed explanation
Since system dissipates its energy gradually, and hence amplitude will also decreases with time according to \(a=a_{0} \mathrm{e}^{-\mathrm{bt/m}}\) \(...(i)\) Energy of vibration drop to half of its in itial value \(\left(\mathrm{E}_{0}\right),\) as…
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