51.

A transformer connected to 220 V mains is used to light a lamp of rating 100 W and 110 V. If the primary current is 0.5 A, the efficiency of the transformer is ( approximately)

• 60 %

• 35 %

• 50 %

• 90 %

Two long parallel wires carrying equal currents which are 8 cm apart produce a magnetic field of 200 µT mid way between them. The magnitude of the current in each wire is

• 10 A

• 20 A

• 300 A

• 40 A

A lamp consumes only 25 % of the peak power in an AC circuit. The phase difference between the applied voltage and the current is

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

The amplitudes E₀ and B₀ of electric and the magnetic component of an electromagnetic wave respectively are related to the velocity c in vacuum as

• ${\mathrm{E}}_0{\mathrm{B}}_0 = \frac{1}{\mathrm{c}}$

• ${\mathrm{E}}_0 = \frac{\mathrm{c}}{{\mathrm{B}}_0}$

• B₀ = cE₀

• E₀ = cB₀

Identify the mismatched pair.

• Microwaves  —  Aircraft navigation

• Radio waves  —  Cellular phone

• γ rays   —  Klystron

• Ultraviolet rays   —  LASIK

A ray of light is incident normally on one refracting surface of an equilateral prism. If the refractive index of the material of the prism is 1.5, then

• the emergent ray is deviated by 30°

• the emergent ray is deviated by 60°

• the emergent ray just graces the second reflecting surface

• the ray undergoes total internal reflection at second refracting surface

The maximum velocities of the photoelectrons ejected are v and 2v for the incident light of wavelength 400 nm and 250 nm on a metal surface respectively. The work function of the metal in terms of Planck's constant h and velocity of light c is

• hc × 10⁶ J

• 2 hc × 10⁶ J

• 1.5 hc × 10⁶ J

• 2.5 hc × 10⁶ J

A radioactive sample contains 10^-3 kg each of two nuclear species A and B with half-life 4 days and 8 days, respectively. The ratio of the amounts of A and B after period of 16 days is

• 1 : 2

• 4 : 1

• 1 : 4

• 2 : 1

The binding energy per nucleon for deuteron (₁H²) and helium (₂He⁴) are 1.1 MeV and 7 .0 MeV, respectively. The energy released when two deuterons fuse to form a helium nucleus is

• 36.2 MeV

• 23.6 MeV

• 47.2 MeV

• 11.8 MeV

In a series of radioactive decays, if a nucleus of mass number 180 and atomic number 72 decays into another nucleus of mass number 172 and atomic number 69, then the number of α and β particles released respectively are

• 2,3

• 2,2

• 2,1

• 2,0