A hollow sphere of external radius R and thickness (t << R) is made of a metal of density ρ. The sphere will float in water, if

• $\mathrm{t} \le \frac{\mathrm{R}}{\mathrm{\rho }}$

• $\mathrm{t} \le \frac{\mathrm{R}}{3\mathrm{\rho }}$

• $\mathrm{t} \le \frac{\mathrm{R}}{2\mathrm{\rho }}$

• $\mathrm{t} \ge \frac{\mathrm{R}}{3\mathrm{\rho }}$

A metal wire of circular cross-section has a resistance R₁. The wire is now stretched without breaking, so that its length is doubled and the density is assumed to remain the same. If the resistance of the wire now becomes R₂ then R₂ : R₁ is

• 1 : 1

• 1 : 2

• 4 : 1

• 1 : 4

Assume that each diode as shown in the figure has a forward bias resistance of 50 Ω and an infinite reverse bias resistance. The current through the resistance 150 Ω is

• 0.66 A

• 0.05 A

• Zero

• 0.04 A

Two particles, A and B, having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii R₁ and R₂, respectively. The ratio of the masses of A and B is

• $\sqrt{{\mathrm{R}}_1/{\mathrm{R}}_2}$

• R₁ / R₂

• (R₁ / R₂)²

• (R₂ / R₁)²

A straight conductor 0.1 m long moves in a uniform magnetic field 0.1 T. The velocity of the conductor is 15 m/s and is directed perpendicular to the field. The emf induced between the two ends of the conductor is

• 0.10 V

• 0.15 V

• 1.50 V

• 15.00 V

A 5 µF capacitor is connected in series with a 10 µF capacitor. When a 300 V potential difference is applied across this combination, the total energy stored in the capacitors is

• 15 J

• 1.5 J

• 0.15 J

• 0.10 J

In the circuit shown below, the switch is kept in position a for a long time and is then thrown to position b. The amplitude of the resulting oscillating current is given by

• $\mathrm{E}\sqrt{\mathrm{L}/\mathrm{C}}$

• E / R

• infinity

• $\mathrm{E}\sqrt{\mathrm{C}/\mathrm{L}}$

28.

A charge q is placed at one corner of a cube. The electric flux through any of the three faces adjacent to the charge is zero. The flux through any one of the other three faces is

• q/3ε₀

• q/6ε₀

• q/12ε₀

• q/24ε₀

Two cells A and B of emf 2V and 1.5 V respectively, are connected as shown in figure through an external resistance 10 Ω. The internal resistance of each cell is 5 Ω. The potential difference E_A and E_B across the terminals of the cells A and B respectively are

• E_A = 2.0 V, E_B = 1.5 V

• E_A = 2.125 V, E_B  = 1.375 V

• E_A = 1.875 V, E_B = 1.625 V

• E_A = 1.875 V, E_B = 1.375 V

Two charges + q and -q are placed at a distance a in a uniform electric field. The dipole moment of the combination is $2\mathrm{qa} \left(\cos \mathrm{\theta } \hat{\mathrm{i}} + \sin \mathrm{\theta } \hat{\mathrm{j}}\right)$, where, θ is the angle between the direction of the field and the line joining the two charges. Which of the following statement(s) is/are correct ?

• The torque exerted by the field on the dipole vanishes

• The net force on the dipole vanishes

• The torque is independent of the choice of coordinates

• The net force is independent of a