When a metal rod of length $l$ is placed in a magnetic field $B$ and moved with velocity $v$ perpendicular to the field,then the induced emf across its ends is

$A$ copper rod of mass $m$ slides under gravity on two smooth parallel rails,with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom,the rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails,as shown in the figure. The terminal speed of the copper rod is

$A$ thin strip $10\, cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5\, N/m$ (see figure). The assembly is kept in a uniform magnetic field of $0.1\, T$. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$. If the mass of the strip is $50\, g$, its resistance $10\, \Omega$ and air drag is negligible, $N$ will be close to:

$A$ wheel with $10$ metallic spokes,each $0.5 \; m$ long,is rotated with a speed of $120 \; rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field $H_{E}$ at a place. If $H_{E} = 0.4 \; G$ at the place,what is the induced $emf$ between the axle and the rim of the wheel? $(1 \; G = 10^{-4} \; T)$

$A$ jet plane is travelling towards west at a speed of $1800\; km/h$. What is the voltage difference developed between the ends of the wing having a span of $25\; m$,if the Earth's magnetic field at the location has a magnitude of $5 \times 10^{-4}\; T$ and the dip angle is $30^{\circ}$ (in $; V$)?

$A$ jet plane of wing span $20 \,m$ is travelling towards west at a speed of $400 \,ms^{-1}$. If the earth's total magnetic field is $4 \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$ at that place, the voltage difference developed across the ends of the wing is (in $\,V$)