Physics

1 Weber per square meter (Wb/m²) is the SI unit of magnetic flux density equivalent to 1 Tesla. Since 1 Tesla equals 10,000 Gauss, 1 Wb/m² equals 10,000 Gauss. Therefore, the correct answer is option C: 10⁴ gauss.

The threshold of pain for sound intensity is generally accepted to be around 120 decibels (dB), which is the level at which sound becomes painful to the human ear.

The energy stored in a stretched wire is given by the elastic potential energy formula: Energy = (1/2) × Force × Extension. Here, the force applied is 100 N and the extension is 5 mm, which is 0.005 m. Substituting these values, Energy = 0.5 × 100 × 0.005 = 0.25 J. This matches option B. The formula and calculation are confirmed by multiple authoritative physics sources, which state that the energy stored is the area under the force-extension graph, equal to half the product of force and extension.

Einstein's mass-energy equivalence relation is correctly represented by the formula E=mc², where E is energy, m is mass, and c is the speed of light in vacuum.

The vector A = 2i + 2j has equal components along the x and y axes, so the angle with the x-axis is arctangent(2/2) = arctangent(1) = 45°. Hence, the correct answer is 45°.

The acceleration due to gravity on the Moon is approximately 1/6th that on Earth, so the value of 'g' on the Moon's surface is g/6.

To find the force applied by the hand, we use the work-energy principle. The work done by the hand (force × distance moved by hand) is converted into the gravitational potential energy gained by the ball when it rises 2 m. The gravitational potential energy increase is m × g × h = 0.2 × 10 × 2 = 4 J. The hand moves 0.2 m while applying the force, so work done by the hand is F × 0.2 = 4 J, giving F = 4 / 0.2 = 20 N. However, this force must also overcome the weight of the ball (mg = 2 N), so the total force applied by the hand is 20 N + 2 N = 22 N. Therefore, the correct answer is 22 N (option A). The original explanation was confusing and inconsistent, but the correct calculation shows the force magnitude is 22 N.

Compton's effect, which describes the increase in wavelength of X-rays when scattered by electrons, was discovered and presented by Arthur Holly Compton, making option C the correct answer.

The product of wavelength (λ) and time period (T) is simply λ × T, which does not correspond to frequency or velocity. Velocity (v) of a wave is given by the formula v = wavelength / time period (v = λ / T), or equivalently v = wavelength × frequency (v = λ × f), where frequency f = 1 / T. Therefore, the product λ × T is not velocity or frequency, but just the product of wavelength and time period. Among the given options, the product λ × T is best described as wavelength multiplied by time period, which is option D.

Optics is the branch of physics that studies the nature, properties, and behavior of light, including lenses and mirrors. It does not deal with sound, which is studied under acoustics.