$A$ 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 $0.40\,G$,the induced $emf$ between the axle and the rim of the wheel is equal to:

$A$ rectangular,a square,a circular,and an elliptical loop,all in the $(x-y)$ plane,are moving out of a uniform magnetic field with a constant velocity,$\vec{V} = v\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf,during the passage of these loops out of the field region,will not remain constant for:

$A$ circular coil of $500$ turns encloses an area of $0.04 \,m^2$. $A$ uniform magnetic field of induction $0.25 \,Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1 \,s$ at a constant angular velocity about one of its diameters. $A$ galvanometer of resistance $25 \,\Omega$ is connected in series with the coil. The total charge that will pass through the galvanometer is.......$C$

$A$ ceiling fan having $3$ blades of length $80 \ cm$ each is rotating with an angular velocity of $1200 \ rpm$. The magnetic field of Earth in that region is $0.5 \ G$ and the angle of dip is $30^{\circ}$. The $EMF$ induced across the blades is $N \pi \times 10^{-5} \ V$. The value of $N$ is:

$A$ metal rod of length $2 \, m$ is rotating with an angular velocity of $100 \, rad/s$ in a plane perpendicular to a uniform magnetic field of $0.3 \, T$. The potential difference between the ends of the rod is.......$V$

$A$ horizontal wire is free to slide on the vertical rails of a conducting frame as shown in the figure. The wire has a mass $m$ and length $l$,and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame,find the terminal speed of the wire as it falls under the force of gravity.