Units & measurements practice · Medium

Option A (Momentum) is correct because both impulse and momentum have the same dimensional formula: [MLT^-1].

Option B (Units but no dimensions) is correct because plane and solid angles are dimensionless quantities but have units (radians and steradians, respectively).

Option C ($\mathrm{Kg}\,{\mathrm{C}^{ - 1}}$) is correct because the electrochemical equivalent (Z) is defined as the mass of the substance deposited per unit charge, so its unit is kg/C or Kg C⁻¹.

Option C is correct because it is the only equation that is dimensionally consistent, with all terms having the dimension of length [L].

Option B (2) is correct because leading zeros are not significant, but trailing zeros after the decimal point are significant.

Option B (Moment of inertia and force) is correct because moment of inertia has dimensions of $ML^2$ while force has dimensions of $MLT^{-2}$, which are not identical.

Option D ($\frac{{3 \pi}}{{2}}$) is correct because 270 degrees is equal to $\frac{{3 \pi}}{{2}}$ radians.

Option B ($5 \alpha^{-1} \beta^{-2} \gamma^2$) is correct because it correctly converts the units of energy from the SI system to the new system.

The correct answer is $\mathrm{LT}{ }^{-2}$ because $\frac{d^2 y}{d x^2}$ represents the second derivative of distance with respect to time, which is acceleration.

Option D (Gravitational constant) is correct because its dimensional formula includes a negative dimension of mass, specifically [M⁻¹L³T⁻²].

Option C is correct because the dimensions of mutual inductance are [ML²T⁻²A⁻²] and the dimensions of capacitance are [M⁻¹L⁻²T⁴A²].

Option D (energy density) is correct because the dimensional formula for x matches the dimensional formula for energy density.

Option D (11%) is correct because the percentage error in kinetic energy is the sum of the percentage error in mass and twice the percentage error in speed.

Option A (The unit of $\lambda$ is same as that of $x$ and $A$) is correct because in the given equation, $\lambda$, $x$, and $A$ all represent lengths and thus have the same unit.

Option C (Vibrations of cesium atom) is correct because Universal Time (UTC) is based on the precise and consistent vibrations of cesium atoms in atomic clocks.

Option C (inversely proportional to unit) is correct because as the size of the unit increases, the numerical value of the quantity decreases, and vice versa.

Option B ($175.1 \mathrm{~cm}^2, 157.6 \mathrm{~cm}^3$) is correct because the surface area and volume are calculated with appropriate significant figures.

Option D (Poisson’s ratio) is correct because Poisson's ratio is dimensionless, while the others have units.

Option D (625) is correct because the density in SI units is 625 kg/m³, which is obtained by converting from CGS units.

Option B (Frequency) is correct because velocity gradient is defined as the change in velocity with respect to distance, resulting in units of inverse time, which is the same as frequency.

Option A ($M{L^2}{T^{ - 2}}$) is correct because couple is the product of force and distance, resulting in the given dimensions.

Option A ($600.1 \mathrm{~mm}$) is correct because it has the smallest percentage error, indicating the highest precision in measurement.

Option B is correct because kilowatt-hour (kWh) is a unit of energy, while Watt-sec, eV, and Js are all units of energy, but kWh is significantly larger.

Option D is correct because Watt is the unit of power, which is the rate of energy transfer, not energy itself.

Option C ($\left[ {{\mathrm{L}^2}{\mathrm{T}^{ - 2}}} \right]$) is correct because $\frac{1}{{{\mu _0}{\varepsilon _0}}}$ represents the square of the speed of light, and speed has dimensions of length/time.

Option A ([LT⁻³],[LT⁻²] and [LT⁻¹]) is correct because it correctly identifies the dimensions of a, b, and c based on the given velocity equation.

Option B ($9.3 \times {10^{ - 6}}{\mathrm{m}^3}$) is correct because the volume is calculated by cubing the length and rounding off to two significant figures.

Option B is correct because both the assertion and the reason are true statements, but the reason does not correctly explain the assertion. The dimensions are calculated correctly, but they are independent statements.

Option D (${x^{ - 2}}$) is correct because if 1 new unit equals x meters, then 1 square meter equals 1/x² in the new units.

Option D ($A{T^2}$) is correct because acceleration is distance over time squared, so length is acceleration times time squared.