21.

Let L be the length and d be the diameter of cross- section of a wire. Wires of the same material with different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum ?

• L = 200 cm, d = 0.5 mm

• L = 300 cm, d = 1.0 mm

• L = 50 cm, d = 0.05 mm

• L = 100 cm, d = 0.2 mm

22320 cal of heat is supplied to 100 g of ice at O°C. If the latent heat of fusion of ice is 80 cal g^-1 and latent heat of vaporization ofwater is 540 cal g^-1, the final amount of water thus obtained and its temperature respectively are

• 8 g, 100°C

• 100 g, 90°C

• 92 g, 100°C

• 82 g, 100°C

A progressive wave moving along x-axis is represented by $\mathrm{y} = \mathrm{A}\hspace{0.17em}\sin \left[\frac{2\mathrm{\pi }}{\mathrm{\lambda }}(\mathrm{vt} - \mathrm{x})\right]$. The wavelength (λ) at which the maximum particle velocity is 3 times the wave velocity is

• A/3

• 2A/(3π)

• $\left(\frac{3}{4}\right)\mathrm{\pi A}$

• (2/3) πA

The magnetic flux linked with a coil satisfies the relation $\mathrm{\varphi } = 4{\mathrm{t}}^2 + 6\mathrm{t} + 9$  Wb, where t is the time in second. The emf induced in the coil at t = 2 s is

• 22 V

• 18 V

• 16 V

• 40 V

A charge +q is placed at the origin O of x-y axes as shown in the figure. The work done in taking a charge Q from A to B along the straight line AB is

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0}\left(\frac{\mathrm{a} - \mathrm{b}}{\mathrm{ab}}\right)$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0}\left(\frac{\mathrm{b} - \mathrm{a}}{\mathrm{ab}}\right)$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0}\left(\frac{\mathrm{b}}{{\mathrm{a}}^2} - \frac{1}{\mathrm{b}}\right)$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0}\left(\frac{\mathrm{a}}{{\mathrm{b}}^2} - \frac{1}{\mathrm{b}}\right)$

What current will flow through the 2 k Ω resistor in the circuit shown in the figure ?

• 3 mA

• 6 mA

• 12 mA

• 36 mA

In a region, the intensity of an electric field is given by E = 2i + 3j+ k in Nc^-1. The electric flux through a surface S = 1Oi m² in the region is

• 5 Nm²C^-1

• 10 Nm²C^-1

• 15 Nm²C^-1

• 20 Nm²C^-1

A straight wire of length 2 m carries a current of 10 A. If this wire is placed in a uniform magnetic field of 0.15 T making an angle of 45° with the magnetic field, the applied force on the wire will be

• 1.5 N

• 3 N

• $3\sqrt{2} \mathrm{N}$

• $\frac{3}{\sqrt{2}} \mathrm{N}$

Two elements A and B with atomic numbers Z_A and Z_B are used to produce characteristic X-rays with frequencies v_A and v_B respectively. If Z_A : Z_B = 1 : 2, then v_A : v_B will be

• $1 : \sqrt{2}$

• 1 : 8

• 4 : 1

• 1 : 4

Two infinite parallel metal planes, contain electric charges with charge densities +σ and -σ respectively and they are separated by a small distance in air. If the permittivity of air is ε₀,then the magnitude of the field between the two planes with its direction will be

• σ/ε₀ towards the positively charged plane

• σ/ε₀ towards the negatively charged plane

• σ/(2ε₀) towards the positively charged plane

• 0 and towards any direction