Physics

In angular motion, Newton's second law is expressed as the net torque (Στ) equals the moment of inertia (I) times the angular acceleration (α), which is option C. Option A is the linear form of Newton's second law, and option B is incorrect. Therefore, option C correctly represents Newton's second law for rotational motion.

The density of human blood is close to that of water, approximately 1.06 g/cm³, making water the best comparison among the options given. Honey, mercury, and kerosene have significantly different densities.

Simple Harmonic Motion (S.H.M.) produces a sinusoidal waveform because the displacement varies sinusoidally with time, characteristic of oscillatory motion governed by sine or cosine functions.

Albert Einstein proposed the concept of the photon as a quantum of light in 1905, explaining the photoelectric effect and introducing the idea that light can be quantized into discrete packets called photons.

A lens that converges parallel rays of light to a single point is called a converging lens, which is typically convex in shape. This is because convex lenses bend light rays inward to meet at the focal point.

The damping in a simple pendulum is primarily caused by the drag force of air, which opposes the motion and gradually reduces the amplitude of oscillation. Gravity and tension in the string are forces that sustain the pendulum's motion rather than cause damping.

In a normal adjustment of an astronomical telescope, the length of the telescope is equal to the sum of the focal lengths of the objective lens (fo) and the eyepiece (fe), i.e., length = fo + fe. This arrangement ensures the final image is at infinity, allowing comfortable viewing.

A seconds pendulum has a time period of 2 seconds. Using the formula T = 2π√(L/g), and taking g ≈ 9.8 m/s², the calculated length comes out to approximately 99.2 cm. Hence, option C is correct.

Michelson's formula for calculating the speed of light is C = 8fd, where f is the frequency of the rotating mirror and d is the distance to the fixed mirror. This formula arises from the time taken for light to travel to the mirror and back, combined with the angular displacement of the rotating mirror.

A photon is defined as a quantum of electromagnetic radiation, meaning it is the smallest discrete amount or packet of electromagnetic energy. It is not a unit of energy, a charged particle, or a unit of wavelength.

Energetic particles in an electron microscope have high kinetic energy, which gives them a very short wavelength and high penetrating power. All these factors contribute to the improved resolution and imaging capability of electron microscopes.

Magnification (M) is calculated as the ratio of the image height to the object height: M = image height / object height. Here, the object height is 5 mm and the image height is 1 cm, which is 10 mm. Therefore, magnification M = 10 mm / 5 mm = 2. This means the image is twice the size of the object, so the correct answer is D (2).

The Compton effect demonstrates that light behaves as particles called photons, as it shows X-rays scattering off electrons with a change in wavelength consistent with particle collisions, thus proving the photon theory of light.

When an object is placed beyond 2f (twice the focal length) of a converging lens, the image formed is real, inverted, and smaller than the object. This is a fundamental property of convex lenses.

In simple harmonic motion (SHM), the total mechanical energy remains constant throughout the motion. This total energy is the sum of kinetic energy and potential energy. The kinetic energy is maximum at the mean (equilibrium) position where the velocity is highest, and the potential energy is maximum at the extreme positions where the displacement is maximum and velocity is zero. Since total energy is conserved and constant at all positions during SHM, it is not maximum at any particular position but remains the same throughout the motion. Therefore, the correct answer is that the energy of SHM is maximum at all positions during SHM.

In the photoelectric effect, the kinetic energy of emitted electrons depends on the frequency (or wavelength) of the incident light, not its intensity. Increasing the intensity increases the number of emitted electrons but does not change their kinetic energy, which remains the same if the wavelength is unchanged.

The Stefan-Boltzmann law (also called Stefan's law) states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature (in Kelvin). This is mathematically expressed as M = σ T^4, where σ is the Stefan-Boltzmann constant. The law is named after Josef Stefan and Ludwig Boltzmann. Planck's law describes the spectral distribution of blackbody radiation but does not express the total energy proportionality to T^4. Wien's law relates to the wavelength at which the emission is maximum, and Rayleigh-Jeans law is an approximation valid at long wavelengths. Therefore, the correct answer is Stefan's law (option C).

The rate of emission of photons is given by the power divided by the energy per photon. Since the energy per photon is E = hc/λ, the rate of emission = P / (hc/λ) = Pλ / (hc). Thus, the rate depends on the wavelength λ, Planck's constant h, speed of light c, and power P, not just a single constant or speed.

In optical fiber transmission systems, repeaters are used to regenerate the dim light signals by amplifying and reshaping them, ensuring the signal can travel long distances without significant loss.

The magnification of an astronomical telescope is given by the ratio of the focal length of the objective lens (fo) to the focal length of the eyepiece (fe), i.e., magnification = fo/fe. This is because the telescope enlarges the angular size of the object by this ratio, making the image appear larger to the observer.

Spherical aberration occurs when light rays passing through a lens near its edge fail to converge at the same point as rays passing near the center, causing a blurred image. This is common in lenses with large apertures. Chromatic aberration, on the other hand, is due to different wavelengths focusing at different points.

A collimator in a spectrometer produces parallel beams of light, which is essential for accurate measurement and analysis of spectra. This ensures that the light entering the spectrometer is well-directed and uniform.

In modern optical fiber communication systems, repeaters or optical amplifiers are typically placed every 20 km to maintain signal strength and quality over long distances. Distances like 100 km or more are generally too long without amplification in newer systems.

A second pendulum is defined as a pendulum with a time period of exactly 2 seconds, meaning it takes 1 second to swing in one direction and 1 second to return, totaling 2 seconds per full oscillation.

The equation θ = 1.22 λ/D describes the angular resolution limit due to diffraction for a circular aperture and is known as the Rayleigh criterion, named after Lord Rayleigh who formulated it.