MHT CET · Physics · Oscillations
A simple pendulum of length ' \(l\) ' has a brass bob attached at its lower end. It's period is ' \(T\) '. A steel bob of the 'same size, having density ' x ' times that of brass, replaces the brass bob. Its length is then so changed that the period becomes ' 2 T '. What is the new length?
- A \(4 / x\)
- B \(\frac{4 l}{x}\)
- C \(4 l\)
- D \(2 l\)
Answer & Solution
Correct Answer
(C) \(4 l\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}} \\
& \Rightarrow \mathrm{~T} \propto \sqrt{l} .
\end{aligned}\)
Time period depends only on effective length. Density has no effect on time period. If time period is made 2 times, then length becomes \(4 l\)
& \mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}} \\
& \Rightarrow \mathrm{~T} \propto \sqrt{l} .
\end{aligned}\)
Time period depends only on effective length. Density has no effect on time period. If time period is made 2 times, then length becomes \(4 l\)
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