Units & measurements practice · Mixed difficulty

Option A (If both assertion and reason are true and the reason is the correct explanation of the assertion) is correct because the units of the Rydberg constant are indeed $m^{-1}$, and this follows directly from the Bohr formula.

Option D is correct because both statements are true, but Statement II does not explain Statement I. Statement II is derived from Statement I using dimensional analysis.

Option D is correct because the dimensional formula of magnetic dipole moment is [L²A], derived from the unit Ampere-meter squared.

Option B ([M¹ L¹ T⁻²]) is correct because force is mass times acceleration, and the dimensions of mass, length, and time are [M], [L], and [T], respectively.

Option D is correct because both angular momentum and Planck's constant have the same dimensions of [ML²T⁻¹].

Option B (Error) is correct because error is defined as the difference between the true value and the measured value of a quantity.

Option D (40) is correct because the density is transformed using the conversion factors for mass and length to the new system of units.

The correct answer is A (If both assertion and reason are true and reason is the correct explanation of assertion) because dimensional homogeneity requires that only quantities with the same dimensions can be added.

Option B (Angular distance between two visible objects) is correct because a sextant is specifically designed to measure angles, particularly the angular distance between celestial objects or between an object and the horizon.

Option B ($\mathrm{Jm}^{-2} \mathrm{~s}^{-1} \mathrm{~K}^{-4}$) is correct because Stefan's constant relates the power radiated per unit area to the fourth power of the temperature.

Option B is correct because impulse is defined as the change in momentum, which has dimensions of mass times velocity ($MLT^{-1}$).

Option D is correct because both the assertion and the reason are false. The measurement 1.30 m is more accurate, and zeros at the end of a number after the decimal point are significant.

Option A ($P$) is correct because dimensional analysis shows that the dimensions of $\frac{a}{b^2}$ are the same as pressure.

Option B ([M⁰ L⁰ T^-1]) is correct because the dimensional formula for (A B C D) is [T^-1] based on dimensional analysis.

Option A (Statement-I is true and statement-II is true) is correct because solid angle is dimensionless and a supplementary quantity, and all supplementary quantities are dimensionless.

Option A (Rotation of earth on its axis) is correct because universal time (UT) is defined based on the Earth's rotation.

Option A is correct because the fringe width in a diffraction pattern is inversely proportional to the diameter of the wire. Increasing the diameter decreases the fringe width.

Option A ($2.95 \times 10^{-40} \mathrm{~m}^3$) is correct because it is the volume calculated using the given radius of the gold nucleus.

Option D (Dimensionless) is correct because relative density is the ratio of two densities, and the dimensions cancel out.

Option C ((A) and (D)) is correct because both energy density and Young's modulus have the same dimensions of $\mathrm{{ML}}^{-1} \mathrm{{T}}^{-2}$.

Option C ([L²MT⁻²]) is correct because Q²/C represents energy stored in a capacitor, which has the same dimensions as energy (ML²T⁻²).

Option C is correct because the unit of magnetic field strength (B) is Tesla (T), which is equivalent to N/A·m or N A⁻¹ m⁻¹.

Option A (Charge) is correct because Faraday is the unit of electric charge, representing the amount of charge carried by one mole of electrons.

Option B (4 min) is correct because the difference between a mean solar day and a sidereal day is approximately 4 minutes.

Option A is correct because the MKS system is indeed a coherent system of units, and in the SI system, the joule is the unit for all forms of energy.

Option A ($\alpha t / \beta$) is correct because it is dimensionless, derived from the principle of homogeneity where the dimensions of each term in the equation must be the same.

Option C ($70.0 \pm \;0.2$) is correct because when subtracting quantities, their absolute errors are added.

Option A (12) is correct because the number of cells in each row is calculated by optimizing the mixed grouping to maximize current through the external resistance.

Option B ($e / 6$) is correct because random error decreases as the number of observations increases.

Option C ($11.7 \mathrm{~cm}^3$) is correct because the volume is calculated using the sphere volume formula and rounded to the correct number of significant figures (3).