MHT CET · Physics · Magnetic Effects of Current
A conducting wire of length \(2500 \mathrm{~m}\) is kept in east-west direction, at a height of \(10 \mathrm{~m}\) from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire \(=25 \sqrt{2} \Omega\), acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}\) )
- A \(0.2\ A\)
- B \(0.02\ A\)
- C \(0.01\ A\)
- D \(2\ A\)
Answer & Solution
Correct Answer
(B) \(0.02\ A\)
Step-by-step Solution
Detailed explanation
\(\text { We know, e }=\mathrm{B} / \mathrm{v} \)
\( \mathrm{v}^2=2 \mathrm{gh} \)
\( \therefore \mathrm{v} =\sqrt{2 \mathrm{gh}} \)
\( \therefore \mathrm{e} =\left(2 \times 10^{-5}\right) \times 2500 \times \sqrt{2 \times 10 \times 10} \)
\( =\left(2 \times 10^{-5}\right) \times 25000 \times \sqrt{2} \)
\( =2 \sqrt{2} \times 25 \times 10^3 \times 10^{-5} \)
\( =50 \sqrt{2} \times 10^{-2} \mathrm{~V} \)
\( \therefore \mathrm{I} =\frac{\mathrm{e}}{\mathrm{R}}=\frac{50 \sqrt{2} \times 10^{-2}}{25 \sqrt{2}}=2 \times 10^{-2}\) \(=0.02 \mathrm{~A}\)
\( \mathrm{v}^2=2 \mathrm{gh} \)
\( \therefore \mathrm{v} =\sqrt{2 \mathrm{gh}} \)
\( \therefore \mathrm{e} =\left(2 \times 10^{-5}\right) \times 2500 \times \sqrt{2 \times 10 \times 10} \)
\( =\left(2 \times 10^{-5}\right) \times 25000 \times \sqrt{2} \)
\( =2 \sqrt{2} \times 25 \times 10^3 \times 10^{-5} \)
\( =50 \sqrt{2} \times 10^{-2} \mathrm{~V} \)
\( \therefore \mathrm{I} =\frac{\mathrm{e}}{\mathrm{R}}=\frac{50 \sqrt{2} \times 10^{-2}}{25 \sqrt{2}}=2 \times 10^{-2}\) \(=0.02 \mathrm{~A}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- When cell of e.m.f. ' \(E_1{ }^{\prime}\) is connected to potentiometer wire, the balancing length is ' \(\ell_1{ }^{\prime}\). Another cell of e.m.f. ' \(E_2{ }^{\prime}\left(E_1>E_2\right)\) is connected so that two cells oppose each other, the balancing length is ' \(\ell_2{ }^{\prime}\). The ratio \(\mathrm{E}_1: \mathrm{E}_2\) isMHT CET 2025 Medium
- For the series LCR circuit, \(R=\frac{X_L}{2}=2 X_c\). The impedance of the circuit and the phase difference between V and I will beMHT CET 2024 Easy
- A vehicle starts from rest and accelerates along straight path at \(2 \mathrm{~m} / \mathrm{s}^2\). At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at \(94 \%\) of its value when the vehicle was at rest?
(speed of sound \(=330 \mathrm{~m} / \mathrm{s}\) )MHT CET 2025 Medium - A simple pendulum starts oscillating simple harmonically from its mean position ( \(\mathrm{x}=0\) ) with amplitude ' a ' and periodic time ' T '. The magnitude of velocity of pendulum at \(X=\frac{a}{2}\) isMHT CET 2025 Medium
- The ratio of the specific heats \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\) in terms of degrees of freedom 'n' is given byMHT CET 2020 Easy
- A closed organ pipe of length ' \(\mathrm{L}_1\) ' and an open organ pipe contain diatomic gases of densities ' \(\rho_1\) ' and ' \(\rho_2\) ' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)MHT CET 2023 Medium
More PYQs from MHT CET
- In the given figure of growth curve identify the phase marked as 'X'.
MHT CET 2022 Hard - If the angle of dip at places \(\mathrm{A}\) and \(\mathrm{B}\) are \(30^{\circ}\) and \(45^{\circ}\) respectively, the ratio of horizontal component of earth's magnetic field at \(A\) to that at \(B\) will be
\([\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}, \quad \sin \frac{\pi}{6}=\frac{1}{2},\) \(\quad \cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}]\)MHT CET 2020 Easy - A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the open air loses half its moisture during the first hour, then the time t , in which \(99 \%\) of the moisture will be lost, isMHT CET 2024 Hard
- Identify the correct statement:
Water flows between two cells__________.MHT CET 2020 Hard - If ' \(\mathrm{E}\) ' is the kinetic energy per mole of an ideal gas and ' \(\mathrm{T}\) ' is the absolute temperature, then the universal gas constant is given asMHT CET 2021 Easy
- Two wavelengths of sodium light \(590 \mathrm{~nm}\) and \(596 \mathrm{~nm}\) are used one after another to study diffraction due to single slit of aperture \(2 \times 10^{-6} \mathrm{~m}\). The distance between the slit and the screen is \(1.5 \mathrm{~m}\). The separation between the positions of first maximum of the diffraction pattern obtained in the two cases isMHT CET 2023 Medium