In a uniform magnetic field of induction B, a wire, in the form of semicircular of radius ‘R’, rotates about the diameter of the circle with an angular speed 'ω' . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R’, the near power generated per period of rotation is (1) \(\frac{B\pi R^2 ω}{2R'}\) (2) \(\frac{(B\pi R^2 ω)^2}{8R'}\) (3) \(\frac{(B\pi Rω)^2}{8R'}\) (4) \(\frac{B\pi R^2ω^2}{8R'}\)

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In a uniform magnetic field of induction B, a wire, in the form of semicircular of radius ‘R’, rotates about the diameter of the circle with an angular speed 'ω' . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R’, the near power generated per period of rotation is (1) \(\frac{B\pi R^2 ω}{2R'}\) (2) \(\frac{(B\pi R^2 ω)^2}{8R'}\) (3) \(\frac{(B\pi Rω)^2}{8R'}\) (4) \(\frac{B\pi R^2ω^2}{8R'}\)

asked Jan 13 by anonymous

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Description : A circular coil, of radius a, (having N turns) is made to rotate about its vertical diameter with an angular speed ω. The coil is present in a region where a uniform horizontal magnetic field B is present. If the coil has a resistance ... a^2 ωB}{\sqrt{2}R}\) and \(\frac{(N\pi a^2 ωB)}{\sqrt{2}R}\)

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Description : A straight rod PQ, of length L, is rotating about an axis passing through O' and perpendicular to its plane. The rod rotates in a uniform (and normal) magnetic field B, with an angular speed ω (The point O' is at a perpendicular ... {BωL^2}{4}\) (3) \(\frac{BωL^2}{3}\) (4) \(\frac{1}{2}BωL^2\)

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Description : A uniform magnetic field B exists in a cylindrical region of radius 0.1 m as shown in the figure. A uniform wire of length 0.80 m and resistance 4.0Ω is bent into a square frame and is placed with one side along a diameter ... frame. [Hint: |ε|= \(\frac{dϕ_B}{dt}=\frac{1}{2}\pi^2\frac{dB}{dt}\) ]

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Description : A mini generator has a coil of 1000 turns, each of area 10-2m2 . The coil is placed with its plane perpendicular to a uniform magnetic field of intensity 25 mT and is rotated at a uniform rate of 100 rotations per ... 3) 100 volt, 0 volt, 100 volt, 0 volt (4) 100 volt, 100 volt, 100 volt, 100 volt

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Description : A conducting circular loop is placed in a uniform magnetic field B = 0.25 T, with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of 1 mm/s. The induced emf, when the radius is 2 cm, ... })μV\) (2) \((\pi)μV\) (3) \((2\pi)μV\) (4) \((2.5)\pi μV\)

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Description : A rod of mass M; length L is made of material of Young's modulus Y. The rod rotates in a horizontal plane about an axis through its one end and perpendicular to length of rod with a constant angular speed ω. The increase in length of ... (\frac{pω^2}{Y})L^3\) (d) \(\frac{2}{3}(\frac{pω^2}{Y})L^3\)

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Description : A rod, PQ, of length l , slides with a constant velocity on two conducting rails. The system of the rod and conducting rails, is present in a region where a uniform (normal) magnetic field, of strength B, is present. The two ... {16Ri_0}{Bl}\) (3) \(\frac{Bl}{(16Ri_0)}\) (4) \(\frac{3Bl}{(16Ri_0)}\)

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Description : A sinusoidal A.C. voltage source, of adjustable frequency, is connected across a series LCR' combination. The inductance (L) and the capacitance (C), present in the circuit, can be expresssed in terms of the quality factor (Q) the ... \(L=\frac{1}{ω_0Q^2R^2}\) and \(C = (\frac{Q^2R^2}{ω_0})\)

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Description : A uniform disc of mass 2m radius R is pivoted at its center O on a smooth horizontal surface. The disc in free to rotate about a vertical axis ZOZ´ through its center O. The disc is initially at rest. A particle of mass m is moving ... \(\frac{2v}{R};\frac{v}{R}\) (4) \(\frac{2v}{R};\frac{v}{2R}\)

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Description : A uniform cylinder of mass M, radius R is rotating about its own axis with a speed of n r.p.s. It is gently placed against a corner as shown in Fig.. Coefficient of freection between walls and cylinder is μ. The number of revolutions ... {48\pi^2μg(μ+1)}\) (4) \(\frac{n^2R(μ^2+1)}{32\pi^2μg(μ-1)}\)

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A voltage source, v = v0 sin ωt, is connected across a series LCR circuit. The values of L and C, in the circuit, equal \(\frac{9R}{ω}\) and \(\frac{1}{10Rω}\) , The phase angle (between the current and voltage in the circuit) and the quality factor, Q, of the circuit, are then equal, respectively, to (1) \(\frac{\pi}{4}\) (Current lagging) and \(2\sqrt{10}\) (2) \(\frac{\pi}{4}\) (Current lagging) and \(3\sqrt{10}\) (3) \(\frac{\pi}{4}\) (Current lagging) and \(3\sqrt{10}\) (4) \(\frac{\pi}{4}\) (Current lagging) and \(2\sqrt{10}\)

Description : A voltage source, v = v0 sin ωt, is connected across a series LCR circuit. The values of L and C, in the circuit, equal \(\frac{9R}{ω}\) and \(\frac{1}{10Rω}\) , The phase angle (between the current and voltage in ... ) and \(3\sqrt{10}\) (4) \(\frac{\pi}{4}\) (Current lagging) and \(2\sqrt{10}\)

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A charge ‘q’ is uniformly distributed on a non-conducting disc, of radius R, it is rotated with angular speed 'ω' about an axis passing through the centre of mass of the disc and perpendicular to its plane. The magnetic moment of the disc will be (1) 1/4 ωqR2 (2) 1/2 ωqR2 (3) ωqR2 (4) 1/8 ωqR2

Description : A charge ‘q’ is uniformly distributed on a non-conducting disc, of radius R, it is rotated with angular speed 'ω' about an axis passing through the centre of mass of the disc and perpendicular to its plane. The magnetic moment of the disc will be (1) 1/4 ωqR2 (2) 1/2 ωqR2 (3) ωqR2 (4) 1/8 ωqR2

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A 10 meter long wire is kept in east west direction. It is falling down with a speed of 5 m/s, perpendicular to the horizontal component of earth’s magnetic field of 0.30 x 10-4 Wb/m2 . (i) what is the momentary p.d induced between the ends of the wire? (ii) which end of the wire will be at a higher potential?

Description : A 10 meter long wire is kept in east west direction. It is falling down with a speed of 5 m/s, perpendicular to the horizontal component of earth's magnetic field of 0.30 x 10-4 Wb/m2 . (i) what ... .d induced between the ends of the wire? (ii) which end of the wire will be at a higher potential?

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A uniform “Catherine Wheel” consists of many thin circular turns of a combustible material. The wheel is free to rotate about a vertical axis through its center in a horizontal plane. The combustile material burns at a constant rate α producing a constant thrust F acting in the tangential direction. The speed, ω, accquired by wheel, starting from rest, when its radius is half of the initial value R is (M0 = Initial mass of Catherine wheel) (1) \(\frac{4\pi FσR}{M_0\alpha}\) (2) \(\frac{2\pi FσR}{M_0\alpha}\) (3) \(\frac{4\pi FσR}{M_1\alpha}\) (4) \(\frac{2\pi FσR}{M_1\alpha}\)

Description : A uniform Catherine Wheel consists of many thin circular turns of a combustible material. The wheel is free to rotate about a vertical axis through its center in a horizontal plane. The combustile material burns at a constant ... (\frac{4\pi FσR}{M_1\alpha}\) (4) \(\frac{2\pi FσR}{M_1\alpha}\)

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A conducting ring, of radius r, is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field, varies, is x, the (average) electric field intensity, at any point of the ring, would be (1) r x (2) rx/2 (3) 2rx (4) 4r/x

Description : A conducting ring, of radius r, is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field, varies, is x, the (average) electric field intensity, at any point of the ring, would be (1) r x (2) rx/2 (3) 2rx (4) 4r/x

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A uniform (normal) magnetic field, B, bends the path of the most energatic photoelectrons, (emitted from a given photosensitive surface due to the action of monochromatic radiations of wave length λ ) into a circle of radius r. The work function, W, for the given photosensitive surface, equals (1) \([\frac{hc}{λ}+\frac{eBr}{2m}]\) (2) \([\frac{hc}{λ}-\frac{eBr}{2m}]\) (3) \([\frac{hc}{λ}-\frac{e^2B^2r^2}{2m}]\) (4) \([\frac{hc}{λ}+\frac{e^2B^2r^2}{2m}]\)

Description : A uniform (normal) magnetic field, B, bends the path of the most energatic photoelectrons, (emitted from a given photosensitive surface due to the action of monochromatic radiations of wave length λ ) into a circle of radius r. The work ... 2r^2}{2m}]\) (4) \([\frac{hc}{λ}+\frac{e^2B^2r^2}{2m}]\)

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A small coil, having n turns each of (everage) radius r, is held normal to the magnetic field liens in the region between the (flat) pole pieces of a horse shoe magnet. The terminals ofthe coil are connected to a special galvanometer that can measure the total charge fleming in the circuit. The coil is taken out of the field region in a (small) time Δt and it is observed that a charge Q flows through the coil-galvanometer circuit. The graph that best shows the dependence of the charge flowing (Q) on the time of withdrawl (Δt) of the coil (from the region of the magnetic field), is the graph labelled as graph. (1) K (2) L (3) M (4) N

Description : A small coil, having n turns each of (everage) radius r, is held normal to the magnetic field liens in the region between the (flat) pole pieces of a horse shoe magnet. The terminals ofthe coil are connected to a ... the magnetic field), is the graph labelled as graph. (1) K (2) L (3) M (4) N

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A wire of mass m is bent into an equilateral triangle of side l . Two beads (identical) each of mass m0 can slide freely along sides PQ and QR of triangle. The triangle is set into rotation about axis ZZ´ and simultaneously beads are let go from point P. As system rotates beads slide down. For the system, what is conserved? (1) Angular speed and total energy (2) Angular momentum and moment of inertia (3) Total energy (i.e. sum of kinetic and potential energy) and total angular momentum (4) Kinetic energy and angular momentum

Description : A wire of mass m is bent into an equilateral triangle of side l . Two beads (identical) each of mass m0 can slide freely along sides PQ and QR of triangle. The triangle is set into ... i.e. sum of kinetic and potential energy) and total angular momentum (4) Kinetic energy and angular momentum

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The magnetic flux, through a coil, present in a magnetic field, directed perpendicular to its plane, varies with time (in second) according to the relation. ϕB = 6t2 + 7t + 1 (ϕB in miliweber) Find the magnitude of the induced emf in the coil at t = 2s. Also find the current, and its direction, in the resistance R, if R = 10Ω

Description : The magnetic flux, through a coil, present in a magnetic field, directed perpendicular to its plane, varies with time (in second) according to the relation. ϕB = 6t2 + 7t + 1 (ϕB in miliweber) Find the ... at t = 2s. Also find the current, and its direction, in the resistance R, if R = 10Ω

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In A.C. voltage source, v = v0 sin t; having a fixed value for v0 , but of variable frequency, is connected across a given series LCR circuit. The variation of the current I, flowing in the circuit, with ω, (the angular frequency ofthe source) is as shown. The power consumption, in the circuit, at (angular) frequencies ω1 and ω2 , is (1) 50% of that at (angular)frequency ω0 and the difference, (ω2- ω1), increases with an increase in the Q-factor of the circuit (2) 50% of that at (angular) frequency ω0 and the difference, (ω2- ω1), decreases with an increase in the Q-factor of the circuit (3) (nearly) 71% of that at (angular) frequency ω0 and the difference, (ω2- ω1) , decreases with an increase in the ‘Q-factor’ of the circuit (4) (nearly) 71% of that at (angular) frequency ω0 a

Description : In A.C. voltage source, v = v0 sin t; having a fixed value for v0 , but of variable frequency, is connected across a given series LCR circuit. The variation of the current I, flowing in the circuit, ... ω0 and the difference, (ω2- ω1) , increases with an increase in the Q-factor' of the circuit

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In A.C. voltage source, v = v0 sin t; having a fixed value for v0 , but of variable frequency, is connected across a given series LCR circuit. The variation of the current I, flowing in the circuit, with ω, (the angular frequency ofthe source) is as shown. The power consumption, in the circuit, at (angular) frequencies ω1 and ω2 , is (1) 50% of that at (angular)frequency ω0 and the difference, (ω2- ω1), increases with an increase in the Q-factor of the circuit (2) 50% of that at (angular) frequency ω0 and the difference, (ω2- ω1), decreases with an increase in the Q-factor of the circuit (3) (nearly) 71% of that at (angular) frequency ω0 and the difference, (ω2- ω1) , decreases with an increase in the ‘Q-factor’ of the circuit (4) (nearly) 71% of that at (angular) frequency ω0 a

Description : In A.C. voltage source, v = v0 sin t; having a fixed value for v0 , but of variable frequency, is connected across a given series LCR circuit. The variation of the current I, flowing in the circuit, ... ω0 and the difference, (ω2- ω1) , increases with an increase in the Q-factor' of the circuit

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A regular polygon of n-sides is formed by bending a wire of total length 2πr. If this wire now carries a current i, the magnetic field B, at the centre of this polygon, would be (1) \(\frac{μ_0in^2 sin^2 (\pi /n)}{2r^2 \pi cos (\pi / n)}\) (2) \(\frac{μ_0in^2 cos^2 (\pi /n)}{2\pi^2 r \,sin (\pi / n)}\) (3) \(\frac{μ_0in^2 sin^2 (\pi /n)}{2\pi^2 r \,cos (\pi / n)}\) (4) zero

Description : A regular polygon of n-sides is formed by bending a wire of total length 2πr. If this wire now carries a current i, the magnetic field B, at the centre of this polygon, would be (1) \(\frac{μ_0in^2 sin^2 (\pi /n)}{2r^2 \pi ... (3) \(\frac{μ_0in^2 sin^2 (\pi /n)}{2\pi^2 r \,cos (\pi / n)}\) (4) zero

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A thin uniform rod AB of mass 2m has length 2L. The rod is pivoted at midpoint O on a smooth horizontal surface. A particle P of mass m moving with speed v0 as shown in Fig ; hits rod at point C and sticks to it. The rod-mass system rotates with an angular speed ω. Then (1) \(v_0=\frac{2}{3}\sqrt{ω}L\) (2) \(v_0=\frac{11}{6}\sqrt{ω}L\) (3) \(v_0=\frac{7}{12}\sqrt{ω}L\) (4) \(v_0=\frac{5}{12}\sqrt{ω}L\)

Description : A thin uniform rod AB of mass 2m has length 2L. The rod is pivoted at midpoint O on a smooth horizontal surface. A particle P of mass m moving with speed v0 as shown in Fig ; hits rod at point C and sticks to it. The rod-mass ... ) (3) \(v_0=\frac{7}{12}\sqrt{ω}L\) (4) \(v_0=\frac{5}{12}\sqrt{ω}L\)

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A given AC source, v = v0 sin ωt, is connected across a given series LCR circuit. The graph, showing simultaneously, the variation of the voltage and current in the circuit, with time, has the form shown. The current, flowing in this circuit, has to be made to have its maximum value (=v/R). This aim can be achieved if, without making any other change in the circuit, we join another inductor (L"), of value (1) \((\frac{1-ω^2 LC}{ω^2C})\) in series with the given inductor (L) (2) \((\frac{1-ω^2 LC}{ω^2C})\) in parallel with the given inductor (L) (3) \((\frac{ω^2 LC}{ω^2C})\) in series with the given inductor (L) (4) \((\frac{ω^2 C}{1-ω^2LC})\) in series with the given inductor (L)

Description : A given AC source, v = v0 sin ωt, is connected across a given series LCR circuit. The graph, showing simultaneously, the variation of the voltage and current in the circuit, with time, has the form shown. The current, ... ) (4) \((\frac{ω^2 C}{1-ω^2LC})\) in series with the given inductor (L)

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An electric current ‘i’ enters, and leaves, a uniform circular wire of radius ‘a’ through diametrically opposite points, A charged particle q, moving along the axis of circular wire, passes through its centre at speed ‘v’. The magnetic force acting on the particle, when it passes through the centre, has a magnitude (1) qv \(\frac{μ_0i}{2a}\) (2) \(qv\,\frac{μ_0i}{4a}\) (3) \(qv\frac{μ_0i}{2\pi a}\) (4) zero

Description : An electric current i' enters, and leaves, a uniform circular wire of radius a' through diametrically opposite points, A charged particle q, moving along the axis of circular wire, passes through its centre at speed v'. The ... \(qv\,\frac{μ_0i}{4a}\) (3) \(qv\frac{μ_0i}{2\pi a}\) (4) zero

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A series LCR circuit is connected to an a.c. voltage source (v = v0 sinωt) and the value of C is such that 1/ωC ≃ 0. The phase angle (θ), between the current flowing and the voltage applied, then equals. (1) tan-1 (ωL/R); current leading; θ can be made zero by taking a value of C equal to \((\frac{1}{ω^2L})\) (2) tan-1 (1/ωLR); current lagging; θ can be made zero by taking a value of C equal to (1/ω2L) (3) tan-1 (1/ωLR); current leading; θ can be made zero by taking a value of C equal to (1/ω2L) (4) tan-1 (1/ωR); current lagging; θ can be made zero by taking a value of C equal to (1/ω2L)

Description : A series LCR circuit is connected to an a.c. voltage source (v = v0 sinωt) and the value of C is such that 1/ωC ≃ 0. The phase angle (θ), between the current flowing and the voltage applied, then equals. (1 ... tan-1 (1/ωR); current lagging; θ can be made zero by taking a value of C equal to (1/ω2L)

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A wire of uniform resistance z r m-1 is sent into a circle of radius r. The same wire is connected between point A and B as shown. The equivalent resistance between A and B is (1) \(\frac{Zr}{(3\pi +16)}\) (2) \(\frac{6\pi (z/r)}{(3\pi +16)}\) (3) \(\frac{6\pi z r}{(3\pi + 16)}\) (4) \((\frac{z}{r})(3\pi + 16)\)

Description : A wire of uniform resistance z r m-1 is sent into a circle of radius r. The same wire is connected between point A and B as shown. The equivalent resistance between A and B is (1) \(\frac{Zr}{(3\pi +16)}\) (2) \(\frac{6\pi (z/ ... (3) \(\frac{6\pi z r}{(3\pi + 16)}\) (4) \((\frac{z}{r})(3\pi + 16)\)

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A thin wire of uniform linear density λ is bent into a semi-circle of radius R. What is the intensity of gravitational field at center O? (1) \(\frac{2GM}{R^2}j\) (2) \(\frac{2GM}{\pi R^2}j\) (3) \(\frac{\sqrt{2}GM}{R^2}j\) (4) \(\frac{3GM}{R^2}j\)

Description : A thin wire of uniform linear density λ is bent into a semi-circle of radius R. What is the intensity of gravitational field at center O? (1) \(\frac{2GM}{R^2}j\) (2) \(\frac{2GM}{\pi R^2}j\) (3) \(\frac{\sqrt{2}GM}{R^2}j\) (4) \(\frac{3GM}{R^2}j\)

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A 100 turn, closely wound circular coil, of mean radius 10cm, carries a current of 3.2 A. The coil is placed in a vertical plane and is free to rotate about a horizontal direction which coinsides with its diameter. A uniform magnetic field, of 2T, in the horizontal direction, exists such that, initially, the axis of the coil is in the direction of the field. The coil rotates through an angle of 90° under the influence of the magnetic field. Calculate the torque in the initial and final position of the coil.

Description : A 100 turn, closely wound circular coil, of mean radius 10cm, carries a current of 3.2 A. The coil is placed in a vertical plane and is free to rotate about a horizontal direction which ... the influence of the magnetic field. Calculate the torque in the initial and final position of the coil.

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Consider two coplanar, co-centric circular coils having radius r1 and r2 (r2 > r1) as shown in the figure. The mutual inductance between these two coils will be (1) \(\frac{μ_0\pi r^2_1}{2r_2}\) (2) \(\frac{μ_0\pi r_1}{2r_2}\) (3) \(\frac{μ_0\pi r^2_2}{2r_2}\) (4) \(\frac{μ_0\pi r^2_1}{2r_1}\)

Description : Consider two coplanar, co-centric circular coils having radius r1 and r2 (r2 > r1) as shown in the figure. The mutual inductance between these two coils will be (1) \(\frac{μ_0\pi r^2_1}{2r_2}\) (2) \(\frac{μ_0\pi r_1}{2r_2}\) (3) \(\frac{μ_0\pi r^2_2}{2r_2}\) (4) \(\frac{μ_0\pi r^2_1}{2r_1}\)

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