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
B.
The density of material is ρ
The hollow sphere will float if its weight is less than the weight of the water displaced by the volume of the sphere. This implies mass of the sphere is less than that for the same volume of water. Now, mass of spherical cell
While the mass of water having same volume
where, ρg = density of water =
For the floatation of sphere,
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
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
E / R
infinity
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 EA and EB across the terminals of the cells A and B respectively are
EA = 2.0 V, EB = 1.5 V
EA = 2.125 V, EB = 1.375 V
EA = 1.875 V, EB = 1.625 V
EA = 1.875 V, EB = 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 , 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