Physics

Microwaves heat substances containing water molecules by causing them to vibrate and generate heat. Milk, containing water, will heat up, but the cup (usually ceramic or glass) may also become warm due to heat conduction from the milk. Therefore, statement (1) that only milk will be heated is false, making option B the correct answer. Statements (2) and (3) are generally true depending on the cup material.

Photons are massless particles; their rest mass is exactly zero. This is a fundamental concept in physics, as photons always travel at the speed of light and cannot be at rest.

When two convex lenses of equal focal length f are placed in contact, their combined focal length F is given by 1/F = 1/f + 1/f = 2/f, so F = f/2.

The least distance of distinct vision, or near point, typically increases with age due to the reduced flexibility of the eye's lens, a condition known as presbyopia. This makes option A correct.

Electrical resonance occurs when inductive and capacitive reactances in a circuit cancel each other, which is a principle used in both radios and microwave ovens for tuning and efficient energy transfer. Therefore, resonance is observed in both devices.

When the lift is in free fall, the effective acceleration due to gravity inside the lift becomes zero. Since the time period of a simple pendulum is T = 2π√(l/g), if g becomes zero, the time period tends to infinity, meaning the pendulum does not oscillate.

According to special relativity, as an object with mass approaches the speed of light, its relativistic mass increases without bound, effectively becoming infinite at the speed of light. This makes it impossible for material objects with mass to reach the speed of light.

The stopping potential depends on the maximum kinetic energy of emitted electrons, which is determined by the frequency of the incident light and the work function of the metal. It does not depend on the intensity or threshold frequency alone.

The uncertainty in momentum and position arises from the fundamental property of matter and radiation described by quantum mechanics, specifically the Heisenberg Uncertainty Principle. This principle states that certain pairs of physical properties cannot both be known to arbitrary precision simultaneously.

The sharpness of resonance, often quantified by the quality factor (Q), is inversely proportional to the damping force. Higher damping reduces the sharpness of resonance, making the system less selective in frequency response.

The natural frequency of a simple pendulum depends on the length of the pendulum and the acceleration due to gravity. Specifically, the frequency is inversely proportional to the square root of the length, not directly the square root of the length itself. Therefore, the correct answer is that it depends on its length.

The Davisson-Germer experiment demonstrated the wave nature of electrons (not protons) by showing electron diffraction patterns when electrons were scattered off a crystal. This confirmed the wave property of matter as predicted by de Broglie.

The dioptre power (P) of a lens is given by the formula P = 100 / focal length (in cm) or equivalently P = 1 / focal length (in meters). For a concave lens, the focal length is negative. Given the focal length is 10 cm, the focal length in meters is 0.10 m, so the power is P = 1 / (-0.10) = -10 dioptres. Therefore, the correct answer is -10 dioptres, which corresponds to option A.

A scanning electron microscope (SEM) produces detailed three-dimensional images of a sample's surface by scanning it with a focused beam of electrons, unlike a standard electron microscope which typically provides two-dimensional images.

The frequency of a second pendulum is defined as one oscillation per two seconds, which corresponds to 0.5 hertz (since frequency is the reciprocal of the period).

A convex lens produces a virtual image only when the object is placed between the principal focus (F) and the optical center (O) of the lens. In this position, the rays diverge after refraction, and the image formed is virtual, erect, and magnified.

When a photon reflects off a mirror, its momentum reverses direction. The change in momentum is therefore twice the magnitude of its initial momentum, making it 'double'.

The relativistic mass m is related to the relativistic energy E by the equation m = E/c², where c is the speed of light. This shows that relativistic mass is energy divided by the square of the speed of light.

Electrons in atoms do not move in simple classical or vibratory motions; instead, their behavior is best described by standing wave patterns (orbitals) according to quantum mechanics. Hence, 'Standing wave motion' correctly describes the electron's motion in an orbit.

The critical angle for glass with a refractive index of about 1.5 (typical for crown glass) when light passes from glass to air (refractive index ~1.0) is calculated using the formula sin(θc) = n2/n1, where n2 is the refractive index of air and n1 is that of glass. This gives sin(θc) = 1/1.5 = 0.6667, so θc = arcsin(0.6667) ≈ 41.8°. Therefore, the critical angle is approximately 42°, making option A the correct answer.

The diameter of a lens is called the aperture, which determines how much light can pass through the lens. The principal axis is an imaginary line through the center of the lens, not its diameter.

The time period T of a simple pendulum is proportional to the square root of its length L, i.e., T ∝ √L. If the length becomes four times, the time period becomes √4 = 2 times the original period.

In Compton scattering, the change in wavelength (Δλ) is given by Δλ = (h/m_ec)(1 - cos θ), where θ is the scattering angle. The maximum change occurs when θ = 180°, as (1 - cos 180°) = 2, the largest possible value.

The Davisson-Germer experiment demonstrated electron diffraction, confirming the wave nature of electrons by showing that electrons produce interference patterns when scattered by a crystal lattice.

Gamma rays (γ-rays) have the highest frequency and thus the highest photon energy among the listed options, making their photons the strongest.