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NEET 2024
Exam
NEET
Year
2024
Subject
Physics
Chapter
Magnetic Effects of Current

NEET 2024 · Physics · Magnetic Effects of Current

In a uniform magnetic field of 0.049 T , a magnetic needle performs...

In a uniform magnetic field of 0.049 T , a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is 9.8×10−6 kg m29.8 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^2. If the magnitude of magnetic moment of the needle is x×10−5Am2x \times 10^{-5} \mathrm{Am}^2, then the value of ' xx ' is : In a uniform magnetic field of 0.049 T , a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The

Options

  1. A128π2128 \pi^2
  2. B50π250 \pi^2
  3. C1280π21280 \pi^2
  4. D5π25 \pi^2

Correct answer

C. 1280π21280 \pi^2

Step-by-step solution

Time period of Oscillation, T=2πIMBT=2 \pi \sqrt{\frac{I}{M B}}⇒14=2π9.8×10−6M×0.049⇒116=4π2×9.8×10−6M×49×10−3⇒M=4π2×9.8×10−649×10−3×16=4π2×9.8×16×10−349=12.8π2×10−3×10−2×102=1280π2×10−5Am2\begin{aligned} & \Rightarrow \quad \frac{1}{4}=2 \pi \sqrt{\frac{9.8 \times 10^{-6}}{M \times 0.049}} \\ & \Rightarrow \frac{1}{16}=4 \pi^2 \times \frac{9.8 \times 10^{-6}}{M \times 49 \times 10^{-3}} \\ & \Rightarrow \quad M=\frac{4 \pi^2 \times 9.8 \times 10^{-6}}{49 \times 10^{-3}} \times 16 \\ & =\frac{4 \pi^2 \times 9.8 \times 16 \times 10^{-3}}{49} \\ & =12.8 \pi^2 \times 10^{-3} \times 10^{-2} \times 10^2 \\ & =1280 \pi^2 \times 10^{-5} \mathrm{Am}^2 \\ & \end{aligned}$$
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