Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Physics
Chapter
Electromagnetic Induction

BITSAT 2011 · Physics · Electromagnetic Induction

A metal rod of length 1 m is rotated about one of its ends in a...

A metal rod of length 1m1 \mathrm{ m} is rotated about one of its ends in a plane right angles to a field of inductance 2.5×10−3Wb/\mathrmm22.5 \times 10^{-3} \mathrm{ Wb} / \mathrmm^{2}. If it makes 1800 revolutions/min. Calculate induced e.m.f. between its ends.

Options

  1. A2.471V2.471 \mathrm{ V}
  2. B3.171V3.171 \mathrm{ V}
  3. C0.471V0.471 \mathrm{ V}
  4. D1.771V1.771 \mathrm{ V}

Correct answer

C. 0.471V0.471 \mathrm{ V}

Step-by-step solution

Given : ℓ=1m,B=5×10−3Wb/\mathrmm2f=180060=30 rotations \ell=1 \mathrm{ m}, \mathrm{ B}=5 \times 10^{-3} \mathrm{ Wb} / \mathrmm^{2}\mathrm{f}=\frac{1800}{60}=30 \text{ rotations }/ sec⁡\mathrm\sec In one rotation, the moving rod of the metal traces a circle of radius r=ℓ∴\mathrm{r}=\ell\therefore Area swept in one rotation =πr2=\pi r^{2}dϕdt=ddt(BA)=B⋅dAdt=Bπ\mathrmr2T=Bfπ\mathrmr2=(5×10−3)×3.14×30×1=0.471V\begin{array}{l}\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{BA})=\mathrm{B} \cdot \frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}=\frac{\mathrm{B} \pi \mathrmr^{2}}{\mathrm{ T}}\\ =\mathrm{B} \mathrm{f} \pi \mathrmr^{2}= \left(5 \times10^{-3}\right)\times3.14 \times30 \times1=0.471 \mathrm{ V} \end{array}$$
Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

Inside a solenoid of radius 0.5 m , magnetic field is changing at a rate of 50 × 10^ -6 T… BITSAT 2024There are two long co-axial solenoids of same length l . The inner and outer coils have… BITSAT 2024A rectangular loop of length 2.5 m and width 2 m is placed at 60^ ^ ∘ to a magnetic field… BITSAT 2024A 12 V battery connected to a coil of resistance 6 Ω through a switch, drives a constant… BITSAT 2023In an LC oscillator, if values of inductance and capacitance become twice and eight… BITSAT 2023A conducting loop of radius 10 π cm is placed perpendicular to a uniform magnetic field… BITSAT 2023A metal disc of radius 100 cm is rotated at a constant angular speed of 60 rad / s in a… BITSAT 2021A conducting square loop of side L and resistance R moves in its plane with a uniform… BITSAT 2020 Full Electromagnetic Induction list All BITSAT PYQs