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

$A$ conducting loop of radius $R$ is present in a uniform magnetic field $B$ perpendicular to the plane of the ring. If radius $R$ varies as a function of time $t$,as $R = R_0 + t$,the e.m.f. induced in the loop is:

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

$A$ circular disc of radius $0.1 \ m$ is rotating about its axis at a frequency of $10 \ rev/s$ in a uniform magnetic field of $0.1 \ T$ directed perpendicular to the disc. Calculate the induced $emf$ between the center and the rim of the disc.

$A$ simple pendulum made of a mass of $10 \ g$ and a metallic wire of length $10 \ cm$ is suspended vertically in a uniform magnetic field of $2 \ T$. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with the vertical, then the maximum induced $EMF$ between the point of suspension and the point of oscillation is . . . . . . $mV$. (Take $g = 10 \ m/s^2$)

An $emf$ of $0.08\,V$ is induced in a metal rod of length $10\,cm$ held normal to a uniform magnetic field of $0.4\,T$,when it moves with a velocity of .......... $m/s$.