Physics

A charge Q is distributed over two concentric conducting thin spherical shells of radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?
(a) the mean free path of the molecules decreases
(b) the mean collision time between the molecules decreases.
(c) the mean free path remains unchanged.
(d) the mean collision time remains unchanged.

The figure shows a region of length 'l' with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 * 10⁵ ms⁻¹ making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, 'l' is close to (mass of proton = 1.67 * 10⁻²⁷ kg, charge of the proton = 1.6 * 10⁻¹⁹C)

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 * 10⁻⁴. The mass of the particle is close to:

When the temperature of metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage change in its mass density will be close to:

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm⁻¹, density = 667 kg m⁻³) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opposite sides of the capillary) make an angle of 60° with one another. Then h is close to (g = 10 ms⁻²)

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of µ?I/π is:

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Rₑ. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √(3/2) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is:

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is

A 750 Hz, 20 V (rms) source is connected to a resistance of 100Ω, an inductance of 0.1803H and a capacitance of 10µF all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to: