Physics Objective Questions and Answers: Units and Dimensions
Review structured MCQ sets for JEE Physics Units and Dimensions. Built according to official JEE guidelines, these downloadable questions support daily revision and core concept reinforcement.
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Multiple Choice Questions
(a) [ML²T⁻¹A⁻¹]
(b) [MT⁻²A⁻¹]
(c) [ML⁻²T⁻¹A⁻¹]
(d) [MLT⁻²A⁻¹]
Show Answer & Explanation
Answer: (b) [MT⁻²A⁻¹]
Explanation:
1. From F = qvB: [B] = [MLT⁻²]/([AT][LT⁻¹]) = [MT⁻²A⁻¹].
Teacher's Note:
1. Tesla = kg s⁻² A⁻¹.
2. Use F = BIl as well.
(a) c²[G e²/(4πε₀)]^(1/2)
(b) (1/c²)[e²/(G 4πε₀)]^(1/2)
(c) (1/c)G e²/(4πε₀)
(d) (1/c²)[G e²/(4πε₀)]^(1/2)
Show Answer & Explanation
Answer: (d) (1/c²)[G e²/(4πε₀)]^(1/2)
Explanation:
1. [e²/(4πε₀)] = [ML³T⁻²], [G] = [M⁻¹L³T⁻²].
2. [G e²/(4πε₀)] = [L⁶T⁻⁴], whose square root is [L³T⁻²]. Dividing by c² = [L²T⁻²] gives [L].
Teacher's Note:
1. Combine the constants step by step.
2. The other options give wrong powers of L.
(a) 0.1 N
(b) 1 N
(c) 10 N
(d) 100 N
Show Answer & Explanation
Answer: (a) 0.1 N
Explanation:
1. Unit of force = 10 g × 10 cm/(0.1 s)² = 100 g cm/0.01 s² = 10⁴ dyne.
2. 10⁴ dyne = 0.1 N.
Teacher's Note:
1. Substitute the new units into F = ma.
2. 1 N = 10⁵ dyne.
(a) Velocity gradient
(b) Pressure gradient
(c) Modulus of elasticity
(d) Thrust
Show Answer & Explanation
Answer: (c) Modulus of elasticity
Explanation:
1. All terms added to p must have the dimension of pressure, so [k] = [ML⁻¹T⁻²].
2. Modulus of elasticity has the same dimension.
Teacher's Note:
1. Terms in the same equation have equal dimensions.
2. Pressure gradient is pressure per length, different from k.
(a) ±0.03 cm³
(b) ±0.111 cm³
(c) ±0.012 cm³
(d) None of these
Show Answer & Explanation
Answer: (a) ±0.03 cm³
Explanation:
1. V = 10.0 × 1.00 × 0.100 = 1.00 cm³.
2. Fractional error = 0.01 + 0.01 + 0.01 = 0.03, so the error is ±0.03 cm³.
Teacher's Note:
1. Each measurement has a 1% error.
2. Add the three fractional errors.
(a) 2%
(b) 1%
(c) 3%
(d) 4%
Show Answer & Explanation
Answer: (c) 3%
Explanation:
1. V = πr²ℓ. Error in ℓ = 0.1/5.0 = 2%; error in r = 0.01/2.00 = 0.5%.
2. Total = 2 + 2 × 0.5 = 3%.
Teacher's Note:
1. The radius appears squared.
2. Use the least count as the absolute error.
(a) [E¹V²T¹]
(b) [E²V⁻²T⁰]
(c) [E¹V⁻²T⁰]
(d) [E⁻¹V²T¹]
Show Answer & Explanation
Answer: (c) [E¹V⁻²T⁰]
Explanation:
1. E = [ML²T⁻²] and V² = [L²T⁻²], so E/V² = [M].
2. Hence [M] = [E V⁻² T⁰].
Teacher's Note:
1. Divide the dimension of energy by that of v².
2. Time does not enter.
(a) [M⁻¹L⁻²T⁴A²]
(b) [ML²T⁻²A⁻²]
(c) [ML²T⁻²A⁻¹]
(d) [MT⁻²A⁻¹]
Show Answer & Explanation
Answer: (a) [M⁻¹L⁻²T⁴A²]
Explanation:
1. C = Q/V = [AT]/[ML²T⁻³A⁻¹] = [M⁻¹L⁻²T⁴A²].
Teacher's Note:
1. Farad = coulomb per volt.
2. Voltage = [ML²T⁻³A⁻¹].
(a) watt-s
(b) kilowatt-hour
(c) eV
(d) J-s
Show Answer & Explanation
Answer: (d) J-s
Explanation:
1. Watt-second, kilowatt-hour and eV are all units of energy.
2. Joule-second is the unit of Planck's constant (angular momentum).
Teacher's Note:
1. Power × time = energy.
2. Compare the dimensions of each.
(a) Wavelength
(b) Pressure
(c) Area
(d) Volume
Show Answer & Explanation
Answer: (c) Area
Explanation:
1. μ is dimensionless, so B/λ² is dimensionless and [B] = [λ²] = [L²].
2. That is the dimension of area.
Teacher's Note:
1. Terms added to a dimensionless number are dimensionless.
2. This is Cauchy's formula.
(a) joule/kelvin
(b) newton-metre
(c) calorie/second
(d) joule/calorie
Show Answer & Explanation
Answer: (a) joule/kelvin
Explanation:
1. Entropy change ΔS = Q/T, so the unit is J K⁻¹.
Teacher's Note:
1. Same as the unit of Boltzmann's constant.
2. Heat divided by temperature.
(a) [ML³T⁻²], [M⁻¹L²T⁻³]
(b) [ML²T⁻¹], [M⁻¹L³T⁻²]
(c) [ML³T⁻²], [M⁻¹L²T²]
(d) [MLT⁻³], [M⁻¹L³T⁻³]
Show Answer & Explanation
Answer: (b) [ML²T⁻¹], [M⁻¹L³T⁻²]
Explanation:
1. h = E/ν has dimension [ML²T⁻¹].
2. G = Fr²/m² has dimension [M⁻¹L³T⁻²].
Teacher's Note:
1. Learn these two standard formulae.
2. Derive from E = hν and Newton's law of gravitation.
(a) Angle
(b) Length
(c) Mass
(d) None of these
Show Answer & Explanation
Answer: (d) None of these
Explanation:
1. [E²L²] = [M²L⁴T⁻⁴][M²L⁴T⁻²] = [M⁴L⁸T⁻⁶], and [M⁵G²] = [M⁵][M⁻²L⁶T⁻⁴] = [M³L⁶T⁻⁴].
2. The ratio is [ML²T⁻²], the dimension of energy, which is not angle, length or mass.
Teacher's Note:
1. Compute powers of M, L and T separately.
2. The result is energy.
(a) [MT⁻³]
(b) [M²LT⁻⁵A⁻²]
(c) [M²LT⁻³A⁻¹]
(d) [MLT⁻²A⁻²]
Show Answer & Explanation
Answer: (b) [M²LT⁻⁵A⁻²]
Explanation:
1. [E] = [MLT⁻³A⁻¹] and [B] = [MT⁻²A⁻¹].
2. [E × B] = [M²LT⁻⁵A⁻²].
Teacher's Note:
1. Multiply the dimensions of the two fields.
2. This is related to the Poynting vector.
(a) Random error
(b) Random as well as systematic error
(c) Systematic error
(d) Neither random nor systematic error
Show Answer & Explanation
Answer: (a) Random error
Explanation:
1. Averaging many readings reduces random errors.
2. Defective weights cause a systematic error, which stays the same however many readings are taken.
Teacher's Note:
1. Systematic errors are not reduced by repetition.
2. Random errors average out.
(a) 0.5%
(b) 5%
(c) 6%
(d) 7%
Show Answer & Explanation
Answer: (b) 5%
Explanation:
1. Error = 2 + 2 × 1 + (1/3) × 3 = 5%.
Teacher's Note:
1. The constant 10 has no error.
2. Cube root gives the power 1/3.
(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation
Answer: (d) 4
Explanation:
1. Density = m/(πr²ℓ).
2. Errors: mass 1%, radius 1%, length 1%. Total = 1 + 2 × 1 + 1 = 4%.
Teacher's Note:
1. Convert each error to a percentage.
2. The radius is squared.
(a) ((n − 1)/n)x
(b) nx/(n − 1)
(c) x/n
(d) x/(n − 1)
Show Answer & Explanation
Answer: (c) x/n
Explanation:
1. 1 VSD = ((n − 1)/n)x, so LC = x − ((n − 1)/n)x = x/n.
Teacher's Note:
1. LC = MSD − VSD.
2. General result: LC = (value of 1 MSD)/(number of vernier divisions).
Assertion (A): Gravitational forces do not depend on the medium between the masses.
Reason (R): The mediating particle responsible for gravitational force is the graviton.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Explanation:
1. Gravitational force depends only on the masses and the distance, so A is true.
2. The graviton is the proposed mediating particle, so R is true, but it does not explain why the medium does not matter.
Teacher's Note:
1. Gravity cannot be screened by any medium.
2. Do not link a statement about the force carrier with the independence from a medium.
Assertion (A): Electrostatic forces are attractive as well as repulsive in nature.
Reason (R): Charges are positive and negative.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. Like charges repel and unlike charges attract.
2. R is true and explains A.
Teacher's Note:
1. Two types of charge give two types of force.
2. Gravity is always attractive.
Assertion (A): Light year and year both measure time.
Reason (R): Light year is the time taken by light to reach the earth from the sun.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (d) A is false, but R is true.
Explanation:
1. A light year is a unit of distance (distance travelled by light in one year), so A is false.
2. R is also false: light takes about 8 minutes from the sun.
Teacher's Note:
1. Light year = 9.46 × 10¹⁵ m.
2. The year is a unit of time.
Assertion (A): All derived quantities may be represented dimensionally in terms of the base quantities.
Reason (R): The dimensions of a base quantity in other base quantities are always zero.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Explanation:
1. Derived quantities are products of powers of the base quantities, so A is true.
2. R is also true (e.g. length has zero power of mass), but it is not the reason for A.
Teacher's Note:
1. Base quantities are independent of each other.
2. Zero power means no dependence.
Assertion (A): If x and y are distances along the x and y axes respectively, the dimensions of d³y/dx³ are [M⁰L⁻²T⁰].
Reason (R): The dimensions of the integral of y dx from a to b are [M⁰L²T⁰].
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Explanation:
1. d³y/dx³ = [L]/[L³] = [L⁻²], so A is true.
2. ∫y dx has dimension [L][L] = [L²], so R is true, but it does not explain A.
Teacher's Note:
1. Derivative divides dimensions; integral multiplies them.
2. Both statements follow separately from the same rule.
Assertion (A): A force can be subtracted from momentum.
Reason (R): Physical quantities with different nature and dimensions can be subtracted.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (d) A is false, but R is true.
Explanation:
1. Force and momentum have different dimensions and cannot be subtracted, so A is false.
2. R is false since only like quantities can be subtracted.
Teacher's Note:
1. Only physical quantities of the same dimensions can be added or subtracted.
2. This is the principle of homogeneity.
Assertion (A): The equation y = 2x + t is physically incorrect if x and y are distances and t is time.
Reason (R): Quantities with different dimensions cannot be added or subtracted.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. 2x has dimension L and t has dimension T, so they cannot be added.
2. R is true and explains A.
Teacher's Note:
1. The principle of homogeneity explains the error.
2. Check each term's dimension.
Assertion (A): The unit vectors i, j and k have units of distance and dimensions [M⁰L¹T⁰].
Reason (R): The product of a scalar and a vector is a new scalar.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (d) A is false, but R is true.
Explanation:
1. Unit vectors are dimensionless and have no unit, so A is false.
2. The product of a scalar and a vector is a vector, so R is false.
Teacher's Note:
1. Unit vectors only give direction.
2. Multiplying a vector by a scalar gives a vector.
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Multiple Choice Questions (MCQs) for JEE Physics Units and Dimensions
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