Free Measurements MCQs with Answers

231. The unit for electric charge is the coulomb, and one Coulomb in terms of the base unit is equivalent to:

• A. Am
• B. Js-1
• C. As
• D. C

Explanation: In terms of SI base units, 1 C is the equivalent of 1 ampere-second, which can be expressed as 1 C = 1 A ⋅ 1 s (or C = A ⋅ s). This can also be thought of as an ampere being equal to 1 coulomb divided by 1 s, as in 1 A = 1 C / 1 s (or A = C / s). In other words, if the current in a circuit is 1 A, 1 C of charge passes through a point in the circuit every second

232. The quantities which can be measured accurately are:

• A. Base Quantities
• B. Physical Quantities
• C. Derived Quantities
• D. Supplementary Quantities

Explanation: Physical Quantities, by definition, are quantities that can be measured with the help of an instrument to give a numerical value with a unit representing the quantity itself.

233. The dimensions of angular acceleration are:

• A. T-2
• B. LT-2
• C. LT-1
• D. M1T-2

Explanation: Angular acceleration (α) is defined as the rate of change of angular velocity (ω) with respect to time (t). Therefore, α = Δω/Δt. The dimension of angular velocity is T-1, so when divided by time (T), the dimension of angular acceleration becomes T-2. This is why the correct answer is T-2.Option B (LT-2) is incorrect because it describes linear acceleration, which involves change in linear velocity rather than angular velocity. Option C (LT-1) is incorrect as it describes velocity, which is a linear measure, not angular. Option D (M1T-2) is incorrect since it is the dimension of force, not relevant to angular acceleration.

234. The dimension of torque are :

• A. (MLT)
• B. (M2 42 L)
• C. (ML2 T-2)
• D. (ML2 T2)

Explanation: The SI unit for torque is the Newton-metre or kgm2sec-2. Torque has the dimension of force times distance, symbolically T−2L2M. Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit newton metre (N⋅m) and never the joule.

235. MLT are are the dimersions of

• A. strain
• B. refractive index
• C. magnification
• D. All of these

Explanation: The given dimensions indicate a dimensional quantity. Strain = change in length/original length [L]/[L] =1 so it is dimensionless Refractive index = velocity of light in medium 1/ velocity of light in medium 2 [LT-1]/[LT-1]=1 so it is dimensionless Magnification=Image length/ Object length [L]/[L] = 1 so it is dimensionless As all these quantities have no dimensions, option D is correct.

236. ML-1T-1 are the dimension of

• A. angular momentum
• B. power
• C. impulse
• D. viscosity

Explanation: The dimensions ML-1T-1 indeed correspond to viscosity. The correct explanation for option D is as follows:Viscosity is a property of fluids that measures their resistance to flow. It determines how easily a fluid can be deformed under the influence of shear stress. The dimensions ML-1T-1 represent viscosity, where:M represents massL represents lengthT represents time In the context of the dimensions ML-1T-1, viscosity is proportional to mass divided by the product of length and time. This indicates that viscosity involves the interactions between mass, length, and time in the context of fluid flow.

237. Ohm x Farad is equivalent to:

• A. Second
• B. Weber
• C. Henry
• D. Tesla

Explanation: The product of Ohm (unit of resistance) and Farad (unit of capacitance) results in the unit of time, which is the second. Therefore, option a is correct.

238. The density of steal ball was determined by measuring the mass and diameter. The mass was measured with 1% and diameter 3% of the error. In the calculated density of the steel ball is at most;

• A. 2%
• B. 8%
• C. 4%
• D. 10%

Explanation: 4%: As mentioned earlier, the maximum error in the calculated density is the sum of the errors in measuring the mass and diameter, which is 1% + 3% = 4%. Therefore, the maximum error in the calculated density is 4%. Based on the analysis, the option that correctly represents the maximum error in the calculated density of the steel ball is 4%.

239. The number of significant figures in 4.0030 is:

• A. Four
• B. Five
• C. Two
• D. Three

Explanation: Five: There are five significant figures in 4.0030. All the digits (4, 0, 0, 3, and 0) are non-zero and the trailing zero after the decimal point indicates precision, making it significant.

240. The uncertainty recorded in the radius of a sphere is 1.6%. The uncertainty in the area of that sphere is:

• A. 4.8%
• B. 3.2%
• C. 1.6%
• D. 0.8%

Explanation: The uncertainty in a measurement involving exponentiation is multiplied by the exponent. For a sphere's area, which is proportional to the square of the radius, the formula for area is A = 4πr2. Therefore, the percentage uncertainty in the area is twice the percentage uncertainty in the radius. Given a 1.6% uncertainty in the radius, the area will have a 2 × 1.6% = 3.2% uncertainty.The incorrect options arise from misunderstanding how uncertainties propagate: 4.8% is calculated as if the exponent was 3, 1.6% is the original uncertainty in the radius, and 0.8% is an incorrect division.