Rotational EMF

Q. A solid cylinder rolls down an inclined plane of inclination 30^°, the acceleration of cylinder is

Q. 2. A particle is projected with speed u at an angle 0with horizontal. In its parabolic path at a point, particle is moving at right angle to initial directionof projection. Its velocity at that point is(2)u cote(1) u tane(3) u cose(4) u cosece

Q. a particle projected from origin moves in x-y plane with a velocity v=3i+6xj where i and j are the unit vectors along x and y axis .find the equation of path followed by the particlr

Q.

A metal conductor of length $1m$ rotates vertically about one of its ends at angular velocity $5$ radians per second. If the horizontal component of the earths magnetic field is $0.2\times {10}^{-4}T$, then the e.m.f developed between the two ends of the conductor is

1. $5\mu V$

2. $50\mu V$

3. $5mV$

4. $50mV$

Q. if the rod PQ rotates with angular speed omega about its midpoint and magnetic field b is out of the plane of motion then the emf induced between pq will be

Q. A ball is projected with velocity 5m/s at an angle of 60^° with horizontal from ground. The speed of the ball at the ins†an t when its velocity is perpendicular to its initial direction of motion is - 1) 5/\surd3 2) 5 3) 5\surd2 4) 10

Q. A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.
EMF induced across the ring is

1. $B\omega R^2$
2. $\frac{B\omega R^2}{2}$
3. $\frac{B\omega R^2}{4}$
4. $2B\omega R^2$

Q. A conducting straight wire $PQ$ of length $l$ is fixed along a diameter of a non-conducting ring as shown in the figure. The ring is given a pure rolling motion on a horizontal surface such that its centre of mass has a velocity $v$. There exists a uniform horizontal magnetic field $B$ in horizontal direction perpendicular to the plane of ring. The magnitude of induced emf in the wire $PQ$ at the position shown in the figure will be

1. $Bvl$
2. $2Bvl$
3. $3Bvl/2$
4. $\text{Zero}$

Q. A 250-turn rectangular coil of length $2.1cm$ and width $1.25cm$ carries a current of 85 $\mu A$ and subjected to a magnetic field of strength $0.85T$. Work done in rotating the coil by ${180}^0$ against the torque is

1. $9.4\mu J$
2. $2.3\mu J$
3. $1.15\mu J$
4. $9.1\mu J$

Q. A wheel with ten metallic spokes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth’s magnetic field at the place. If the magnitude of the field is 0.4 Gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to

1. $1.256\times {10}^{-3}$V
2. $6.28\times {10}^{-4}$V
3. $1.256\times {10}^{-4}$ V
4. $6.28\times {10}^{-5}$ V

Q. A wire of length $l$, mass $m$ and resistance $R$ slide without any friction down the parallel conducting rails of negligible resistance. The rails are connected to each other at the bottom by a rail of negligible resistance which is parallel to the wire . The wire and rail forms a closed rectangular conducting loop. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform magnetic field $B$ which exists throughout the region. Find the steady velocity of the wire.

1. $\frac{mg\text{sin}\theta }{R{B}^2{l}^2{\cos }^2\theta }$
2. $\frac{mg{\sin }^2\theta }{R{B}^2{l}^2{\cos }^2\theta }$
3. $\frac{mgR\text{sin}\theta }{B^2{l}^2{\cos }^2\theta }$
4. $\frac{mgR{\sin }^2\theta }{B^2{l}^2{\cos }^2\theta }$

Q. A conducting rod AC of length $4l$ is rotated about a point 0 in a uniform magnetic field field $\overrightarrow{B}$ directed into the paper. $AO=l$ and $OC=3l$ , then

1. $V_A-V_0=\frac{B\omega l^2}{2}$
   
2. $V_0-V_C=\frac{7B\omega l^2}{2}$
   
3. $V_C-V_0=\frac{9B\omega l^2}{2}$
   
4. $V_A-V_C=4B\omega l^2$

Q. A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. AO = l and OC = 3l. Then

1. $V_A-V_O=\frac{B\omega l^2}{2}$
   
2. $V_O-V_C=\frac{7}{2}B\omega l^2$
   
3. $V_A-V_C=4B\omega l^2$
   
   
4. $V_C-V_O=\frac{9}{2}B\omega l^2$
   

Q. 26. What should be the angular speed with which theearth have to rotate on its axis so that a person ornthe equator would weigh th as much aspresent?(1) 5R352R2) 5g2g2 R2g5R15g

Q. If a coil rotates in a uniform magnetic field about the axis along the plane of the coil then why does the magnetic flux linked through the coil change when we know that in a uniform magnetic field when a conductor gradually enters, the magnetic flux changes but when the conductor has completely reached the magnetic field and it is still moving in the uniform magnetic field then the magnetic flux does not change?

Q. A concentric spherical cavity is cut out from a solid conducting sphere and a charge $+Q$ is placed at the centre of the cavity. The magnitude of net electric field $E$ and net potential $V$ at point $A$ is

1. $E=0,V=0$
2. $E=0,V=\frac{3kQ}{2R}$
3. $E=\frac{kQ}{R^2},V=\frac{kQ}{2R}$
4. $E=0,V=\frac{kQ}{2R}$

Q. Find the variation of ${ϵ}_{ind}$ vs time for the following system.

1. 
2. 
3. 
4. 

Q. a ball is projected with speed 50 m/s at an angle of 53 degree . find its speed and angle with acceleration vector of the projectile at t=3s

Q.

An ant slides from point (0, 0) to (3, 4, 6) under the wind force $\overrightarrow{F}=(2x\hat{i}+4\hat{j}+6z\hat{k})$. Find the work

done by the force of wind in Joules.

__

Q. A rod of length L is rotating with an angular velocity $\omega$ in a uniform magnetic field $B_0$ as shown in figure. Potential difference between the ends of rod A and B is
(Take $OB=\frac{L}{4}$)

1. $B\omega L^2$
2. $\frac{B\omega L^2}{2}$
3. $\frac{B\omega L^2}{3}$
4. $\frac{B\omega L^2}{4}$

Q. If $\overrightarrow{B_1},\overrightarrow{B_2}$ and $\overrightarrow{B_3}$ are the magnetic field due to the wires carrying current $I_1,I_2$ and $I_3$, then in the expression of Ampere's circuital law, $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$, $\overrightarrow{B}$ is

Q. A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is

1. $B\omega l^2$
   
2. $\frac{1}{2}B\omega l^2$
   
3. $\frac{1}{8}B\omega l^2$
   
4. Zero

Q. A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$)

1. $\frac{B{R}^2\alpha t}{2}$
2. $\frac{3B{R}^2\alpha t}{2}$
3. $\sqrt{3}B{R}^2\alpha t$
4. $\frac{B{R}^2\alpha t}{\sqrt{2}}$

Q. A square metal wire loop of side $10cm$ is moved with a constant velocity $v$ in a uniform magnetic field $B=2Wb{m}^{-2}$ as shown in figure. The magnetic field lines are perpendicular to the plane of the loop and directed into the plane. The loop is connected to the network of resistances, each of value $3\Omega$. The resistance of the other wires are negligible. The speed of the loop so as to have a steady current of $1mA$ in the loop is

1. $1cm{s}^{-1}$
2. $4cm{s}^{-1}$
3. $1.5cm{s}^{-1}$
4. $0.5cm{s}^{-1}$

Q. Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

1. $0$
2. $8Bvr$
3. $4Bvr$
4. $16Bvr$