Physics Questions and Answers

Answer: B

The focal length of a thin lens follows the lens maker's formula, \(1/f = (n_{rel} - 1)(1/R_1 - 1/R_2)\), where \(n_{rel}\) is the index of the lens relative to the surrounding medium. In air \(n_{rel} = 1.5\), so \(1/f_a = 0.5\,K\). In medium A, \(n_{rel} = 1.5/1.4\), so \(1/f_m = (1.5/1.4 - 1)K = 0.0714\,K\). Dividing:

The lens becomes much weaker because the glass and medium have nearly equal indices. The options 0.21 m and 0.11 m would need the focal length to shrink, which cannot happen when the surrounding index rises toward that of the lens.

Answer: B

The continuity equation in electromagnetism relates the time rate of change of charge density to the current density: \[ \nabla\cdot\mathbf{J} = -\frac{\partial\rho}{\partial t} \] It states that charge is conserved, so the charge leaving a volume is balanced by the fall in the charge inside. The key gives electric potential, which is not the quantity in the equation, and so the key is not in agreement with the standard form; the standard answer would be the current density.

Answer: B

Boyle's law says that at constant temperature the pressure of a fixed amount of an ideal gas is inversely proportional to its volume, that is \(PV = \text{constant}\). Halving the volume doubles the pressure. The options that say pressure is directly proportional to volume are wrong because they reverse the relation, and the options that speak of constant pressure and of force describe a different law, since Boyle's law holds the temperature fixed and relates pressure and volume.

Answer: D

A car on top of a hill, a compressed spring and a bent bow all store energy because of their position or condition, and that is potential energy. It turns to kinetic energy when the car rolls down or the spring and bow are released.

Kinetic energy is the energy of motion and the car is not moving, and chemical energy is stored in fuel and food. Mechanical energy is the sum of potential and kinetic energy, so it is not the specific name for stored energy of this kind.

Answer: B

Mercury is a fluid, because it is a liquid at room temperature and flows. Wood, marble and glass are treated as solids in the question: wood and marble are rigid solids, and glass, though it is an amorphous solid, does not flow at ordinary temperatures.

A fluid is any substance that can flow, meaning a liquid or a gas, and mercury is the only option that is one.

A fluid is any substance that flows and takes the shape of its container, and it includes liquids and gases. Mercury is the only metal that is liquid at ordinary room temperature, so it is the one fluid on the list. Wood and marble hold a fixed shape, and glass is an amorphous solid whose very slow flow is not seen at room temperature.

Answer: A

The distance between the centre of a compression and the centre of the adjacent rarefaction is half the wavelength. A wavelength is the distance between two successive compressions (or two successive rarefactions), and a rarefaction lies midway between two compressions.

Twice the wavelength, the wavelength itself and one-third of the wavelength do not match that geometry.

A wavelength is the full distance between two compressions, so the point midway between them is a rarefaction, half a wavelength away.

Answer: B

The momentum increases by 20 per cent. Kinetic energy is p squared over 2m, so for a given mass the momentum is proportional to the square root of the kinetic energy. A 44 per cent rise makes the energy 1.44 times, and the square root of 1.44 is 1.2, so the momentum becomes 1.2 times, an increase of 20 per cent. A 10 per cent rise gives only 1.21 times the energy, 22 per cent gives 1.49 times, and 44 per cent would need the energy to be 2.07 times.

Answer: A

Kinetic energy is half the mass times the square of the velocity.

\[ KE = \tfrac{1}{2} m v^{2} \]

\[ KE = \tfrac{1}{2} \times 30 \times 64 = 960\ \mathrm{J} \]

So the object has 960 J of kinetic energy, option (A). The value 120 J comes from using the velocity without squaring it (15 x 8), and 480 J and 240 J come from mistakes in squaring or halving, so they are wrong. The kinetic energy therefore depends on the square of the speed, so doubling the speed of this object to 16 metres per second would increase its energy fourfold, to 3840 J.

Answer: A

Malus' Law belongs to the study of light, in particular polarisation: it says that the intensity of plane-polarised light passing through an analyser varies as the square of the cosine of the angle between the polarisation direction and the analyser axis. Gravity, surface tension and inertia belong to mechanics and fluids, so they are not the subject of this law. In symbols, \[ I = I_{0}\cos^{2}\theta \] where \(I_0\) is the intensity of polarised light reaching the analyser and \(\theta\) is the angle between the polarisation direction and the analyser axis.

Answer: B

The curie is a unit of radioactivity.

One curie is \(3.7\times10^{10}\) disintegrations per second, originally the activity of one gram of radium-226. The SI unit is the becquerel, one disintegration per second.