Units & Dimensions

10 NEET-UG practice questions on Units & Dimensions, part of Physics. The first 10 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. Question 1 · Hard

   Suppose force F, acceleration A and time T are chosen as the base quantities of a system of units. In this system, what are the dimensions of angular momentum?

   1. A[F A² T³]
   2. B[F A T³]
   3. C[F A⁻¹ T³]
   4. D[F A T²]

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   Answer: B · [F A T³]

   Mass = F/A and length = AT² (from acceleration × time²). Angular momentum = mass × length²/time = (F/A)(A²T⁴)/T = FAT³. Check: angular momentum = length × linear momentum = (AT²)(FT) = FAT³.

   • A: This takes mass as F instead of F/A.
   • C: This writes length with a wrong power of A.
   • D: This gives the dimensions of energy, F × length.

   Remember this

   First write mass and length in the new base quantities, then substitute into the usual formula.

2. Question 2 · Medium

   Match List-I with List-II. List-I (quantity) A. Young's modulus B. Coefficient of viscosity C. Torque D. Planck's constant List-II (dimensional formula) I. [ML²T⁻¹] II. [ML⁻¹T⁻¹] III. [ML⁻¹T⁻²] IV. [ML²T⁻²]

   1. AA-II, B-III, C-I, D-IV
   2. BA-II, B-III, C-IV, D-I
   3. CA-III, B-II, C-I, D-IV
   4. DA-III, B-II, C-IV, D-I

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   Answer: D · A-III, B-II, C-IV, D-I

   Young's modulus is stress, [ML⁻¹T⁻²]. Viscosity from F = ηA(dv/dx) is [ML⁻¹T⁻¹]. Torque has the dimensions of energy, [ML²T⁻²], and Planck's constant, E/ν, is [ML²T⁻¹].

   • A: This makes both of the swaps above.
   • B: This swaps Young's modulus and viscosity, which differ by one power of T.
   • C: This swaps torque and Planck's constant.

   Remember this

   Planck's constant has the dimensions of angular momentum; torque has the dimensions of energy.

3. Question 3 · Medium

   A screw gauge has a pitch of 0.5 mm and 50 circular divisions. With the jaws closed and nothing between them, it already reads 0.04 mm. For a wire, the pitch scale shows 1.5 mm and circular division 28 is on the reference line. What is the true diameter of the wire?

   1. A1.78 mm
   2. B1.60 mm
   3. C1.82 mm
   4. D1.74 mm

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   Answer: D · 1.74 mm

   Least count = 0.5/50 = 0.01 mm, so the observed reading = 1.5 + 28 × 0.01 = 1.78 mm. The gauge reads 0.04 mm too much, so the true value = 1.78 − 0.04 = 1.74 mm.

   • A: This ignores the zero error.
   • B: This takes the least count as half its true value.
   • C: This adds the zero error instead of subtracting it.

   Remember this

   True reading = observed reading − zero error, keeping the sign of the zero error.

4. Question 4 · Hard

   An empty beaker has a mass of (50.0 ± 0.1) g. With a liquid in it, the mass is (90.0 ± 0.1) g. The volume of the liquid is (20.0 ± 0.1) cm³. How should the density of the liquid be reported?

   1. A(2.00 ± 0.3) g/cm³
   2. B(2.00 ± 0.02) g/cm³
   3. C(2.00 ± 0.015) g/cm³
   4. D(2.00 ± 0.01) g/cm³

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   Answer: B · (2.00 ± 0.02) g/cm³

   Mass of liquid = 40.0 g, and in a difference the absolute errors add: ±0.2 g, which is 0.5%. The volume error is 0.1/20 = 0.5%, so density has a 1% error. Density = 40.0/20.0 = 2.00 g/cm³, and 1% of it is ±0.02.

   • A: This adds absolute errors in the quotient instead of relative errors.
   • C: This uses only ±0.1 g for the mass found by subtraction.
   • D: This subtracts the two mass errors, so only the volume error remains.

   Remember this

   Add absolute errors for a sum or difference; add relative errors for a product or quotient.

5. Question 5 · Medium

   Which pair of physical quantities has the same dimensional formula?

   1. APressure and force
   2. BSurface tension and spring constant
   3. CTorque and angular momentum
   4. DImpulse and kinetic energy

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   Answer: B · Surface tension and spring constant

   Surface tension is force per unit length and the spring constant is force per unit extension, so both are [MT⁻²].

   • A: Pressure is force per unit area, so it differs from force by [L⁻²].
   • C: Torque is [ML²T⁻²] but angular momentum is [ML²T⁻¹].
   • D: Impulse is [MLT⁻¹] but kinetic energy is [ML²T⁻²].

   Remember this

   Force per unit length gives [MT⁻²], whatever the physical setting.

6. Question 6 · Easy

   Twenty divisions on the sliding scale of a measuring instrument span the same length as nineteen main scale divisions of 1 mm each. Find the least count of the instrument.

   1. A0.1 mm
   2. B0.5 mm
   3. C0.95 mm
   4. D0.05 mm

   Answer and explanation in LearnFree account

7. Question 7 · Easy

   A student records the mass of a metal pellet as 0.0050200 kg. How many significant figures does this reading have?

   1. A6
   2. B5
   3. C8
   4. D3

   Answer and explanation in LearnFree account

8. Question 8 · Medium

   Arrange the following quantities in increasing order of the power of length L in their dimensional formulae. A. Pressure B. Impulse C. Angular momentum D. Surface tension

   1. AD, A, C, B
   2. BA, B, D, C
   3. CA, D, B, C
   4. DD, A, B, C

   Answer and explanation in LearnFree account

9. Question 9 · Easy

   From Newton's law of gravitation, what is the dimensional formula of the gravitational constant G?

   1. A[M⁻¹L³T⁻²]
   2. B[M⁻²L³T⁻²]
   3. C[ML³T⁻²]
   4. D[M⁻¹L²T⁻²]

   Answer and explanation in LearnFree account

10. Question 10 · Medium

    To find g with a simple pendulum, a student measures the length as (80.0 ± 0.2) cm and the time for 40 oscillations as (64.0 ± 0.4) s. Using g = 4π²L/T², what is the percentage error in g?

    1. A1.0%
    2. B0.875%
    3. C1.25%
    4. D1.5%

    Answer and explanation in LearnFree account