Q169 / 180 · COMEDK 2015 · Physics
A $10 \mathrm{~kg}$ collar is attached to a spring (spring constant $600 \mathrm{~N} / \mathrm{m}$ ), it slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $20 \mathrm{~cm}$ and released. What is the speed of the oscillation?
- Correct answerA$\sqrt{60} \times 0.2 \mathrm{~m} / \mathrm{s}$
- B$60 \times 0.2 \mathrm{~m} / \mathrm{s}$
- C$60 \times 2 \mathrm{~m} / \mathrm{s}$
- D$6 \times 0.2 \mathrm{~m} / \mathrm{s}$
Solution
Given, amplitude, $A=20 \mathrm{~cm}=0.2 \mathrm{~m}$
Force constant, $k=600 \mathrm{Nm}^{-1}$
Maximum speed of oscillation,
$\begin{aligned} v_{\max } &=A \omega \\ &=A \sqrt{\frac{k}{m}} \quad\left[\because \omega=\sqrt{\frac{k}{m}}\right] \\ &=0.2 \sqrt{\frac{600}{10}}=0.2 \sqrt{60} \mathrm{~m} / \mathrm{s} \end{aligned}$
Hence, the correct answer is option: 'A'.