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 .......... $m/s$.

$A$ coil of area $80 \, cm^2$ and $50$ turns is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05 \, T$. The maximum value of the e.m.f. developed in it is

$A$ conducting rod $PQ$ of length $5\,m$ oriented as shown in the figure is moving with velocity $(2\,m/s)\hat{i}$ without any rotation in a uniform magnetic field $(3\hat{j} + 4\hat{k})\,T$. The $Emf$ induced in the rod is.....$V$.

Statement-$I$: When a conducting rod moves in a uniform transverse magnetic field with a uniform speed which is perpendicular to its length,then a potential difference may develop across its ends.
Statement-$II$: In any conductor,free electrons and free positive ions are available.

$A$ straight conductor of length $0.4 \ m$ is moving with a speed of $7 \ ms^{-1}$ perpendicular to a magnetic field of intensity $0.9 \ Wb \ m^{-2}$. The induced emf across the conductor will be (in $V$)

$A$ 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: