Physics

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.

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.

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.

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.

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.

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.

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.

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 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.

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.