A bicycle wheel of diameter ' $D$ ' has ' $N$ ' number of spokes. Wheel is rotating at the rate of ' $x$ ' revolutions per minute, perpendicular to the horizontal component of earth's magnetic field ' $\mathrm{B}_{\mathrm{H}}$ '. The e.m.f. induced between the rim and the centre of the wheel will be
$\frac{\mathrm{B}_{\mathrm{H}} \pi \mathrm{Dx}}{120}$
$\quad \frac{\mathrm{B}_{\mathrm{H}} \pi \mathrm{Dx}}{240}$
$\frac{B_H \pi D^2 x}{240}$
$\quad \frac{\mathrm{B}_{\mathrm{H}} \pi \mathrm{D}^2 \mathrm{x}}{120}$
Four thin rods of same mass M and same length L form a square as shown in figure. Moment of inertia of this system about an axis passing through point O and perpendicular to its plane is

$\frac{4}{3} \mathrm{ML}^2$
$\frac{\mathrm{ML}^2}{3}$
$\frac{\mathrm{ML}^2}{6}$
$\frac{2}{3} \mathrm{ML}^2$
Two spherical black bodies of radius $\mathrm{R}_1$ and $\mathrm{R}_2$ with surface temperatures $\mathrm{T}_1$ and $\mathrm{T}_2$ respectively. If $T_1=2 T_2$ and they radiate the same power then relation between $R_1$ and $R_2$ is
$R_2=8 R_1$
$\mathrm{R}_2=\mathrm{R}_1$
$R_2=2 R_1$
$R_2=4 R_1$
A simple pendulum has mass 2 gram and charge $2 \mu \mathrm{C}$. In a uniform horizontal electric field of intensity $1000 \mathrm{~V} / \mathrm{m}$, pendulum is at rest. At equilibrium, the angle made by the pendulum with the vertical is ( $\mathrm{g}=$ acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )
$\tan ^{-1}(0.2)$
$\tan ^{-1}(0.1)$
$\tan ^{-1}(0.4)$
$\tan ^{-1}(0.5)$
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