Physics

The fundamental frequency of an open pipe is twice that of a closed pipe of the same length because an open pipe supports a full wavelength, while a closed pipe supports only a quarter wavelength, resulting in fopen = 2 × fclosed.

The trajectory of a projectile under the influence of gravity, neglecting air resistance, is a parabola. This is because the horizontal motion is uniform while the vertical motion is uniformly accelerated, resulting in a parabolic path.

According to Newton's theory, sound travels in air under adiabatic conditions because the compression and rarefaction of air during sound propagation occur too rapidly for heat exchange, making the process adiabatic rather than isothermal.

In liquids and gases, electric current is carried by the movement of both negative charges (electrons or anions) and positive charges (cations). This is because these media contain ions of both polarities that move under an electric field, producing current.

Sound waves are mechanical waves that require a material medium (solid, liquid, or gas) to propagate. Since a vacuum lacks any material particles, sound cannot travel through it.

The production of heat when an electric current passes through a conductor is known as the Joule effect, named after James Prescott Joule. This phenomenon explains how electrical energy is converted into heat energy in resistive materials.

A motorcycle safety helmet extends the time over which the collision occurs, thereby reducing the force acting on the head according to the impulse-momentum theorem (Force = change in momentum / time). This reduction in force helps prevent injury.

The velocity of sound in air varies with temperature approximately as v = v0 * sqrt(T/T0), where T is the absolute temperature in Kelvin. At 0°C (273 K), the speed of sound is about 331 m/s. To double this velocity, the temperature must be such that the speed is twice 331 m/s, i.e., 662 m/s. Since velocity is proportional to the square root of absolute temperature, we have 662 = 331 * sqrt(T/273), which implies sqrt(T/273) = 2, or T/273 = 4, so T = 4 * 273 = 1092 K. Converting to Celsius, 1092 K - 273 = 819°C. Therefore, the velocity of sound in air doubles its velocity at 0°C at approximately 819°C, which corresponds to option C.

Using Bragg's law nλ = 2d sinθ with n=1, d=2×10⁻¹⁰ m, and θ=30°, the wavelength λ = 2 × 2×10⁻¹⁰ × sin30° = 2 × 2×10⁻¹⁰ × 0.5 = 2×10⁻¹⁰ m. However, the question states 'glancing angle' which is complementary to θ, so θ = 90° - 30° = 60°. Using θ=60°, λ = 2 × 2×10⁻¹⁰ × sin60° ≈ 3.46×10⁻¹⁰ m, closest to option A (4×10⁻¹⁰ m). Therefore, option A is correct.

The periodic alternation of sound between maximum and minimum loudness is known as beats. Beats occur due to the interference of two sound waves of slightly different frequencies, causing the sound intensity to vary periodically.

In the double slit experiment, light passing through two slits produces an interference pattern due to the superposition of waves from each slit. Additionally, each slit acts as a source of diffraction, so the observed pattern is a combination of both interference and diffraction fringes.

Beats occur due to the phenomenon of constructive and destructive interference between two sound waves of slightly different frequencies, causing periodic variations in sound intensity.

Specific resistance (resistivity) is an intrinsic property of the material and does not depend on the wire's length or radius. It depends solely on the type of material.

Higher-wattage incandescent bulbs have filaments that are thicker (have a larger cross-sectional area) to reduce electrical resistance, allowing more current to flow at the same voltage. This thicker filament is necessary to handle the higher power rating. For example, a 60W bulb has a thinner filament compared to a 200W bulb, which has the thickest filament among the given options.

The photoelectric effect was explained by Albert Einstein, who proposed that light consists of quanta called photons, which can eject electrons from a metal surface. This explanation earned him the Nobel Prize in Physics in 1921.

One kilowatt hour (kWh) is defined as the amount of energy delivered when one kilowatt of power is used continuously for one hour. Therefore, the correct time duration is one hour.

Internal resistance is the resistance offered by the source of EMF (such as a battery or cell) to the flow of current within itself. It is an inherent property of the source, not of external components like conductors, resistors, or capacitors.

Sound requires a medium (solid, liquid, or gas) to propagate as it travels by vibrating particles. In a vacuum, there are no particles to transmit sound waves, so the velocity of sound is zero.

The blue color of the sky is caused by Rayleigh scattering, where shorter blue wavelengths of sunlight are scattered more than other colors by the molecules in the atmosphere.

Newton's laws of motion are classical mechanics laws that accurately describe the motion of particles at everyday speeds. However, they fail for particles moving at velocities close to the speed of light, where relativistic effects become significant and special relativity must be used instead.

A potential divider circuit provides a continuously varying output voltage (potential) by dividing the input voltage in proportion to the resistances. This is why it is called a potential divider.

At absolute zero (0 K), the thermal vibrations of atoms in a conductor cease, causing the resistance to drop to nearly zero. This is because resistance in conductors primarily arises from lattice vibrations, which are absent at absolute zero.

The frequency of a simple pendulum is independent of the mass of the bob. It depends only on the length of the pendulum and gravity. Therefore, replacing the bob with a heavier one does not change the frequency; it remains f.

In metallic conductors, electric current is primarily due to the flow of free electrons, which are negatively charged particles that move through the metal lattice when a potential difference is applied. Protons and neutrons do not move freely in a conductor, and the mechanism is well established, so it is not under controversy.

A fuse is designed to protect electrical circuits by breaking the circuit when the current exceeds a safe level, thus preventing damage from high current. It does not directly protect against high voltage or overheating, although it indirectly prevents overheating by stopping excessive current.