Units and Measurements

The SI unit of electric current is the ampere, which measures the flow of electric charge per second. Coulomb is the unit of electric charge, and volt is the unit of electric potential difference.

The elastic modulus (Young's modulus) has the same dimensions as pressure or stress, which is force per unit area. Force has dimensions MLT^-2, and area has dimensions L^2, so the dimension of elastic modulus is ML^-1T^-2.

Electrical energy is measured in kilowatt-hours (kWh), which represents the amount of energy consumed when one kilowatt of power is used for one hour. The other options are units of power or incorrect terms.

In a Michelson Interferometer, moving one mirror by a distance d changes the optical path length by 2d because the light travels to the mirror and back. Each fringe observed corresponds to a change in path length equal to one wavelength λ. Therefore, the number of fringes m observed when the mirror moves by d is given by m = 2d / λ. Given d = 0.5 mm = 500,000 nm and m = 2000 fringes, the wavelength λ = 2d / m = (2 × 500,000 nm) / 2000 = 500 nm. Since 1 nm = 10 Å, 500 nm = 5000 Å. Among the options, 5000 Å (option B) correctly represents the wavelength of the light used. Option A (5000 nm) is incorrect as it is 10 times larger than the correct value. Options C and D are not relevant units for wavelength in this context.

One megawatt hour (MWh) is equal to 1,000,000 watts multiplied by 3600 seconds, which equals 3.6 x 10^9 joules. This is confirmed by multiple authoritative sources. Therefore, the correct answer is option C: 36 x 10^9 J (which is equivalent to 3.6 x 10^10 J, but the intended meaning is 3.6 x 10^9 J). The originally marked answer A (36 x 10^6 J) is incorrect as it equals 3.6 x 10^7 J, which is much smaller than the actual value.

Stress, Young's modulus, and pressure all have the dimensions of force per unit area (N/m² or Pascal). Strain, however, is a dimensionless quantity representing deformation relative to original length, so it does not have dimensions of force per unit area.

The metre was historically defined in terms of the wavelength of the red cadmium spectral line, a definition established by Albert A. Michelson. This definition linked the unit of length to a specific physical constant, improving precision in measurements.

Power is defined as the rate of doing work or energy transfer per unit time. Since work has the dimension [ML^2T^{-2}] and time has the dimension [T], power has the dimension [ML^2T^{-3}].

Work and torque both have the same dimensional formula, which is M L^2 T^-2. This is because work is force times distance and torque is force times lever arm distance, so their dimensions match.

One horsepower (hp) is defined as exactly 746 watts (W). This is a standard conversion used in physics and engineering to relate mechanical power to electrical power.

Torque and energy both have the same dimensional formula M L² T⁻². Momentum and impulse both have dimensions M L T⁻¹. Energy and work have identical dimensions M L² T⁻². Mass has dimension M, while moment of inertia has dimension M L². Therefore, the pair that does not have identical dimensions is mass and moment of inertia, making option D the correct answer.

The magnitude of vector A = 2i - 2j + k is calculated as √(2² + (-2)² + 1²) = √(4 + 4 + 1) = √9 = 3. The unit vector in the direction of A is the vector divided by its magnitude, which is (2i - 2j + k)/3. Therefore, the correct option is C.

1 Tesla (T) is equal to 10,000 Gauss (G), so the correct relationship is 1T = 10^4 G. This is a standard unit conversion in magnetism.

The potential difference across the galvanometer is calculated using Ohm's law: V = IR. Given the resistance R = 100 Ω and the current I = 20 mA = 0.02 A, the potential difference V = 0.02 × 100 = 2 volts. Therefore, the correct answer is option C (2 volt).

A unit vector denoted as n^ typically represents a normal vector to a surface, meaning it is perpendicular to that surface. This is a standard notation in physics and vector mathematics.

The magnitude of the vector $𝐀=2\hat{i}-2\hat{j}+\hat{k}$ is calculated as $\sqrt{2^2+(-2{)}^2+1^2}=\sqrt{4+4+1}=\sqrt{9}=3$. The unit vector in the direction of $𝐀$ is the vector divided by its magnitude, which is $\frac{2}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{1}{3}\hat{k}$. This corresponds to option C, $\frac{2\hat{i}-2\hat{j}+\hat{k}}{3}$. Therefore, the correct answer is C.

The SI unit of magnetic flux density (B) is the tesla (T). One tesla is defined as one weber per square meter (Wb/m²). It can also be expressed in base SI units as newton per ampere per meter (N·A⁻¹·m⁻¹). Among the given options, option B (NAm-1) corresponds to newton per ampere per meter, which is the correct SI unit representation for magnetic flux density. Therefore, the correct answer is B, not D.

Torque and energy do not have identical dimensions; torque has dimensions of force times distance (ML²T⁻²) but is a vector, while energy is a scalar with the same dimensional formula but different physical meaning. Momentum and impulse share the same dimensions (MLT⁻¹), energy and work are dimensionally identical (ML²T⁻²), and mass and moment of inertia differ since moment of inertia has dimensions of mass times length squared (ML²).

The expression cosθ î + sinθ ĵ represents a vector of unit length pointing at an angle θ from the x-axis, which is the definition of a unit vector in that direction.

The International System of Units (SI) primarily consists of two types of units: base units and derived units. Base units are fundamental, while derived units are combinations of base units.

Measurement errors can arise from multiple sources including human inexperience, faulty equipment or apprentices, and inappropriate methods. Therefore, all the reasons listed in options A, B, and C can cause errors in measurement.

Uncertainty in measurement can arise from multiple sources including the limitations of the measuring instrument, natural variations in the object being measured, and inadequate measurement techniques. Therefore, all options A, B, and C contribute to measurement uncertainty.

The dimensional formula ML⁻¹T⁻² corresponds to force per unit area, which is the dimension of pressure. Force has the dimension ML¹T⁻², and dividing by area (L²) gives ML⁻¹T⁻². This dimension also corresponds to energy per unit volume, but among the given options, pressure is the correct match. Momentum has the dimension MLT⁻¹, energy has ML²T⁻², and force has ML¹T⁻², so they do not match ML⁻¹T⁻².

The number 0.0173 has three significant figures: 1, 7, and 3. Leading zeros are not counted as significant figures.

The dimension of force is given by mass × acceleration. Mass has dimension M, and acceleration has dimension LT⁻², so force has dimension MLT⁻², which corresponds to option B.