21.

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K= 5/3 is inserted between the plates, the magnitude of the induced charge will be:

• 0.9 n C

• 1.2 n C

• 0.3 n C

• 2.4 n C

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B₂. The ratio B₁/B₂ is:

• $\frac{1}{\sqrt{2}}$

• 2

• $\sqrt{3}$

• $\sqrt{2}$

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r_∝ respectively in a uniform magnetic field B. The relation between r_e, r_p, r_∝ is:

• r_e < r_∝ < r_p

• r_e > r_p =  r_∝

• r_e < r_p =  r_∝

• r_e < r_p <  r_∝

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 kΩ. How much was the resistance on the left slot before interchanging the resistances?

• 910Ω

• 990Ω

• 505Ω

• 550 Ω

In a potentiometer experiment, it is found that no current passes through the galvanometer when the
terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a
resistance of 5Ω, a balance is found when the cell is connected across 40 cm of the wire. Find the internal
resistance of the cell.

• 2.5 Ω

• 1 Ω

• 1.5 Ω

• 2 Ω

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2.Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

• 60°

• 0°

• 30°

• 45°

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?

• 2 x 10⁶

• 2 x 10⁵

• 2 x 10⁴

• 2 x 10⁵

An electron from various excited states of hydrogen atom emits radiation to come to the ground state. Let λ_n, λ_g, be the de Broglie wavelength of the electron in the n^th state and the ground state respectively. Let Λ_n be the wavelength of the emitted photon in the transition from the n^th state to the ground state. For large n, (A, B are constants)

• ${\Lambda }_n^2 \approx \lambda$

• ${\Lambda }_n \approx A + \frac{B}{{\lambda }_n^2}$

• ${\Lambda }_n \approx A + B{\lambda }_n$

• ${\Lambda }_n^2 \approx A + B{\lambda }_n^2$

If the series limit frequency of the Lyman series is vL, then the series limit frequency of the Pfund series is:

• v_L/25

• 25v_L

• 16 v_L

• v_L/16

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 μm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance?
(i.e. distance between the centres of each slit.)

• 100 μm

• 25 μm

• 50 μm

• 75 μm