21.

The temperature of the black body increases from T to 2T. The factor by which the rate of emission will increase, is?

• 4

• 2

• 16

• 8

The dimensional formula for Young's modulus is

• $\left[\mathrm{M} {\mathrm{L}}^{-1} {\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{M}}^{\mathrm{o}} \mathrm{L} {\mathrm{T}}^{-2}\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{-2}\right]$

• $\left[\mathrm{M} {\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown.

• $1:\sqrt{2}$

• 1:3

• 1:2

• $\sqrt{3}:1$

A conducting sphere of radius R = 20 cm is given by a charge Q = 16μC. What is E at centre?

• 3.6×10⁶ N/C

• 1.8×10⁶ N/C

• Zero

• 0.9×10⁶ N/C

A coil having N turns carry a current as shown in the figure. The magnetic field intensity at point  P 

• $\frac{{\mathrm{\mu }}_0{\mathrm{NiR}}^2}{2{\left({\mathrm{R}}^2+{\mathrm{x}}^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{Ni}}{2\mathrm{R}}$

• $\frac{{\mathrm{\mu }}_0 {\mathrm{NiR}}^2}{{\left(\mathrm{R}+\mathrm{x}\right)}^2}$

• Zero

An electron moves at right angle to a magnetic field of 1.5×10^-2 T with a speed of 6 x 10⁷ m / s. If the specific charge of the electron is 1.7x 10¹¹ C/ kg. The radius of the circular path will be

• 2.9 cm

• 3.9 cm

• 2.35 cm

• 2 cm

The potential difference between point A and B is

• $\frac{20}{7 } \mathrm{V}$

• $\frac{40}{7}\mathrm{V}$

• $\frac{10}{7}\mathrm{V}$

• zero

When a certain current is passed in the circuit as shown in figure, 10 kcal of heat is produced in 5 Ω resistance. How much heat is produced in 4 Ω resistance?

• 4 kcal

• 2 kcal

• 5 kcal

• 3 kcal

If an insulated non-conducting sphere of radius R has charge density ρ. The electric field at a distance r from the centre of sphere (r > R) will be

• $\frac{\mathrm{\rho } \mathrm{R}}{3{\mathrm{\epsilon }}_{\mathrm{o}}}$

• $\frac{\mathrm{\rho } \mathrm{r}}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

• $\frac{\mathrm{\rho } \mathrm{r}}{3 {\mathrm{\epsilon }}_{\mathrm{o}}}$

• $\frac{3 \mathrm{\rho } \mathrm{R}}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

An L.C. circuit is in the state of resonance. If C = 0.1F and L = 0.25 Henry. Neglecting ohmic resistance of circuit. What is the frequency of oscillations?

• 1007 Hz

• 100 Hz

• 100 Hz

• 500 Hz