MHT CET · Physics · Oscillations
Three masses \(500 \mathrm{~g}, 300 \mathrm{~g}\) and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is also removed it will oscillate with a period of
- A 1 s
- B 1.5 s
- C 2 s
- D 2.5 s
Answer & Solution
Correct Answer
(A) 1 s
Step-by-step Solution
Detailed explanation
When 500 g is removed, \(\mathrm{m}=(100+300) \mathrm{g}=0.4 \mathrm{~kg}\)
\(\begin{array}{ll}
\therefore & T=2 \pi \sqrt{\frac{0.4}{k}}=2 s \\
\Rightarrow & \frac{2 \pi}{\sqrt{k}}=\frac{2}{\sqrt{0.4}} \quad \ldots (i)
\end{array}\)
When 300 g is also removed,
\(\begin{aligned}
m^{\prime} & =100 g=0.1 \mathrm{~kg} \\
\therefore T^{\prime} & =2 \pi \sqrt{\frac{0.1}{k}}=\frac{2}{\sqrt{0.4}} \sqrt{0.1} \quad \text { (using Eq. (i)) } \\
T^{\prime} & =\frac{2}{2}=1 s
\end{aligned}\)
\(\begin{array}{ll}
\therefore & T=2 \pi \sqrt{\frac{0.4}{k}}=2 s \\
\Rightarrow & \frac{2 \pi}{\sqrt{k}}=\frac{2}{\sqrt{0.4}} \quad \ldots (i)
\end{array}\)
When 300 g is also removed,
\(\begin{aligned}
m^{\prime} & =100 g=0.1 \mathrm{~kg} \\
\therefore T^{\prime} & =2 \pi \sqrt{\frac{0.1}{k}}=\frac{2}{\sqrt{0.4}} \sqrt{0.1} \quad \text { (using Eq. (i)) } \\
T^{\prime} & =\frac{2}{2}=1 s
\end{aligned}\)
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