Units & measurements practice · Medium

Option D (Becquerel) is correct because Becquerel is the SI unit of radioactivity, not length.

Option D is correct because strain is a dimensionless quantity, being the ratio of two lengths.

Option B (If both assertion and reason are true but reason is not the correct explanation of assertion) is correct because both the assertion about linear mass density's dimensions and the reason about density are true, but the reason doesn't explain the assertion.

Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because force and pressure have different dimensions, so they cannot be added.

Option C ((ii) and (iii)) is correct because both pressure and Young's modulus have the same dimensional formula, which is [ML⁻¹T⁻²].

Option B (4) is correct because the trailing zeros after the decimal point are significant.

Option D is correct because dimensional analysis shows that a/b² has the same dimensions as pressure.

Option B (${\mathrm{M}{\mathrm{T}^{ - 2}}}$) is correct because surface tension is force per unit length, and its dimensions are mass times time to the power of -2.

Option B (time) is correct because the ratio L/R has dimensions of time, and the product RC also has dimensions of time.

The correct answer is B (Pressure) because stress is defined as force per unit area, which is the same as pressure.

Option B ($\frac{\mathrm{J}}{\mathrm{m}^2 \mathrm{~s}}$) is correct because the Poynting vector represents power per unit area, which is measured in Watts per square meter (W/m²), equivalent to Joules per second per square meter (J/m²s).

Option D (Both (1) and (3)) is correct because the equation is dimensionally correct but numerically incorrect as the refractive index is always greater than 1.

Option D (32%) is correct because it is the relative error in P calculated using the given relative errors in a, b, c, and d.

Option B is correct because dimensional analysis can only determine relationships with up to three independent variables.

Option A ($\frac{1}{100(N+1)}$) is correct because the vernier constant is the difference between one main scale division and one vernier scale division.

The correct answer is Spring oscillator because it has the lowest frequency among the given options, making it unsuitable for measuring small time intervals.

Option D (Selecting instrument with small least count) is correct because a smaller least count allows for more precise measurements, reducing accidental errors.

Option A is correct because the expression is dimensionless, representing the fine-structure constant.

Option C (0.1) is correct because the conversion factor from CGS to MKS for Young's modulus is 0.1, derived from the unit conversion of dyne/cm² to N/m².

The correct answer is C (Dimensionless) because the coefficient of friction is a ratio of two forces, making it dimensionless.

Option B (Momentum and Planck’s constant) is correct because momentum has dimensions of [MLT⁻¹] while Planck's constant has dimensions of [ML²T⁻¹], which are different.

Assertion is correct because changing units changes the numerical value. Reason is incorrect because smaller units have larger numerical values.

Option C is correct because the gravitational constant G has units of $N m^2 kg^{-2}$, derived from the gravitational force equation.

Option C (0.5 mm) is correct because the pitch is calculated by multiplying the least count by the number of divisions on the circular scale.

Option B (60 micron) is correct because 0.00006 m is equal to 60 micrometers.

Option D (If the assertion and reason both are false) is correct because rate of flow is volume per unit time, not velocity, and its dimensions are [L³T⁻¹], not [MLT].

Option A (The maximum value of $Y$ that can be determined is $10^{14} \mathrm{~N} / \mathrm{m}^2$) is false because the calculated Young's modulus is significantly lower than this value, given the provided parameters and uncertainties.

Option C (Fermi) is correct because 1 Fermi is equal to 10^-15 meters, which is the smallest unit among the given options.

Option B ($36 \times {10^5}J$) is correct because 1 kWh is equal to 1000 watts multiplied by 3600 seconds, which results in $36 \times {10^5}$ Joules.

Option B ([M⁰ L⁰ T⁰]) is correct because γ is a dimensionless quantity, being the ratio of two specific heats.