MHT CET · Physics · Magnetic Effects of Current
A magnetic needle of magnetic moment \(6 \times 10^{-2} \mathrm{Am}^2\) and moment of inertia \(9.6 \times 10^{-5} \mathrm{~kg} \mathrm{~m}^2\) performs simple harmonic motion in a magnetic field of 0.01 T . Time taken to complete 10 oscillations is [Take \(\pi=3 \cdot 14\) ]
- A 0.2512 s
- B 2.512 s
- C 25.12 s
- D \(251 \cdot 2 \mathrm{~s}\)
Answer & Solution
Correct Answer
(C) 25.12 s
Step-by-step Solution
Detailed explanation
Period of oscillation \(T=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}\)
\(\begin{aligned}
& =2 \pi \sqrt{\frac{9.6 \times 10^{-5}}{6 \times 10^{-2} \times 0.01}} \\
& =2.512 \mathrm{~s}
\end{aligned}\)
\(\therefore \quad\) Time taken for 10 oscillations \(=2.512 \times 10\)
\(=25.12 \mathrm{~s}\)
\(\begin{aligned}
& =2 \pi \sqrt{\frac{9.6 \times 10^{-5}}{6 \times 10^{-2} \times 0.01}} \\
& =2.512 \mathrm{~s}
\end{aligned}\)
\(\therefore \quad\) Time taken for 10 oscillations \(=2.512 \times 10\)
\(=25.12 \mathrm{~s}\)
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