An elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to uniform magnetic field $\mathrm{B}=0.6 \mathrm{~T}$. When loop is released, the radius starts shrinking at constant rate $3 \mathrm{~cm} / \mathrm{s}$. The induced e.m.f. in the loop at an instant when the radius of the loop is 10 cm will be (in mV )
$2.6 \pi$
$3.6 \pi$
$3.2 \pi$
$1.8 \pi$
Two solid spheres of same material but of mass ' M ' and ' 8 M ' fall simultaneously through a viscous liquid. Their terminal velocities are respectively ' V ' and ' nV '. The value ' n ' is
2
4
8
16
Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop is ' $x B$ '. The value of ' $x$ ' is ( $\mu_0=$ permeability of vacuum or free space)
$\frac{\sqrt{A^3}}{\mu_0 \pi}$
$\frac{2 \sqrt{A}}{\mu_0 \pi}$
$\frac{2}{\mu_0} \sqrt{\frac{\mathrm{~A}^3}{\pi}}$
$\frac{2}{\mu_0} \sqrt{\frac{\mathrm{~A}}{\pi}}$
An ideal gas in a container of volume 500 cc is at a pressure of $2 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. The average kinetic energy of each molecule is $6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is
$5 \times 10^{25}$
$5 \times 10^{23}$
$25 \times 10^{23}$
$2.5 \times 10^{22}$
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