NEET Units and Measurements Previous Year Questions with Solutions

For a standard Vernier calliper where 10 Vernier scale divisions equal 9 main scale divisions:

• • 1 MSD = 1 mm.
• • LC = 0.1 mm = 0.01 cm.

When the Vernier zero lies to the LEFT of the main scale zero, the error is negative. By NCERT convention:

• • N = 10 (total divisions on Vernier scale).
• • n = 4 (coinciding division).
• • True zero error is -0.06 cm.

Actual length equals observed reading minus zero error:

• • However, the options printed by NTA were: (1) 0.60 cm, (2) 0.96 cm, (3) 1.00 cm, (4) 1.04 cm.
• • The correct scientific answer 1.06 cm was missing because the question setter erroneously calculated error as -4 * LC = -0.04 cm (giving Option 4) or subtracted it (giving Option 2).
• • During answer key challenge review, NTA accepted the flaw and awarded FULL MARKS to all candidates (Key: A,B,C,D).

From Stefan's law for radiant energy emitted per unit area per second:

• • Radiant energy per second is Power: [M L^2 T^-3].
• • Dividing by area [L^2] and temperature to the fourth [K^4] gives [M T^-3 K^-4].

From kinetic theory of gases and Wien's displacement law:

• • Wien's law: lambda_{max} * T = b ==> [b] = [L K].

Combine all three dimensional terms:

• • Mass: M^{1 - 1} = M^0 (mass cancels completely).
• • Length: L^{-2 + 1} = L^{-1}.
• • Time: T^{-3 + 2} = T^{-1}.
• • Temperature: K^{-4 + 1 + 1} = K^{-2}.
• • Final combined dimension: [L^-1 T^-1 K^-2].
• • Matches Option (1) exactly.

The least count (LC) of a vernier calliper is the difference between one main scale division and one vernier scale division:

• • LC = 1 MSD - 1 VSD = 0.1 cm - 0.09 cm = 0.01 cm.

The total observed reading before zero error correction is given by the main scale reading plus the vernier scale contribution:

• • Raw measurement on the scales reads 5.08 cm.

When the jaws are closed, the zero mark of the vernier scale lies at +0.1 cm to the right of the main scale zero. This is a positive zero error (+0.1 cm). The true reading is obtained by subtracting the zero error:

• • Matches Option (3) with absolute precision.

For a physical quantity defined by P = a^p b^q c^r d^s, logarithmic differentiation gives the maximum fractional error:

• • Here p = 3, q = 2, r = -1, s = -1/2.
• • The negative signs become positive because errors compound in the worst-case direction.

Multiply both sides by 100 to convert to percentage errors:

• • Substitute given values: a = 1%, b = 3%, c = 2%, d = 4%.

Compute the algebraic sum:

• • Matches Option (3) exactly.

The Vernier Constant (also known as the Least Count) of a Vernier caliper is the difference between the length of one main scale division (MSD) and one vernier scale division (VSD):

We are given that (N + 1) divisions of the vernier scale coincide with N divisions of the main scale:

Substituting 1 VSD into the definition of VC:

We are given 1 MSD = 0.1 mm. Expressing this in centimeters:

Substituting 1 MSD = 1/100 cm into the VC equation:

Solid angle Ω subtended by an area element dA at distance r is defined as the ratio of area to the square of distance:

Strain ε is defined as fractional change in dimension (e.g. change in length per unit original length):

Plane angle θ is defined as the ratio of arc length to radius:

Evaluating the other quantities present in distractors: - Arc: [L] - Stress: [Force / Area] = [M L⁻¹ T⁻²] - Angular speed: [Angle / Time] = [T⁻¹] Only the pair "strain and angle" are both dimensionless [M⁰L⁰T⁰].

According to Fourier’s principle of dimensional homogeneity, physical quantities can be added or equated only if they have the same dimensions. In the force equation F = αt² + βt, both terms on the right must independently have dimensions of force [M L T⁻²]:

Solving for the dimensional formulas of α and β:

Solving for the dimensions of β:

Evaluating the dimensions of the expression αt / β:

In physics measurements, experimental errors are broadly categorized into Systematic Errors and Random Errors:

According to the standard NCERT physics syllabus, random errors are errors that occur irregularly and are random with respect to sign and size. They arise due to unpredictable fluctuations in experimental conditions such as voltage supply variations, temperature fluctuations, and mechanical vibrations.

Instrumental errors arise from zero error or calibration defects; Personal errors arise from human bias or parallax; Least count errors are associated with instrument resolution. None of these arise from unpredictable ambient fluctuations.

A wire is modeled as a uniform cylinder of mass m, radius r, and length L. Its volume is V = π r² L. The density ρ is defined as mass per unit volume:

Taking the natural logarithm and differentiating to obtain the maximum relative (fractional) error, where errors always add up to give the upper bound:

Convert each measurement uncertainty into percentage error (% = Δx / x × 100):

Substitute the percentage errors into the total error formula (noting the power of 2 for radius):

The least count is the smallest distance moved by the spindle corresponding to one circular scale division:

Using the standard screw gauge reading formula with zero zero-error mentioned:

Since $1\text{ cm} = 10\text{ mm}$, divide the reading by 10:

Energy has the dimensions of work (Force $\times$ Displacement):

From Newton's universal law of gravitation $F = G \frac{m_1 m_2}{r^2}$:

Divide the dimensional formula of $E$ by that of $G$ using the laws of indices:

Assume the dimensional formula of energy in terms of $[F]$, $[A]$, and $[T]$ is given by:

The standard SI dimensional formulae for the quantities are: - $[E] = [M^1 L^2 T^{-2}]$ - $[F] = [M^1 L^1 T^{-2}]$ - $[A] = [M^0 L^1 T^{-2}]$ - $[T] = [T^1]$

Equating powers of $M$, $L$, and $T$ on both sides: 1. Power of $M$: $x = 1$ 2. Power of $L$: $x + y = 2 \implies 1 + y = 2 \implies y = 1$ 3. Power of $T$: $-2x - 2y + z = -2 \implies -2(1) - 2(1) + z = -2 \implies -4 + z = -2 \implies z = 2$

The pitch of a screw gauge is the linear distance advanced by the screw on the main scale when the circular cap/thimble is rotated through one complete revolution ($$360^\circ$$). The least count ($$\text{LC}$$) is the smallest distance that can be measured using the instrument, given by: $$\text{LC} = \frac{\text{Pitch}}{\text{Total number of divisions on circular scale } (N)}$$

$$\text{Pitch} = \text{LC} \times N$$

Given: - Least count = $$0.01\text{ mm}$$ - Total circular scale divisions $$N = 50$$ $$\text{Pitch} = 0.01\text{ mm} \times 50 = 0.50\text{ mm} = 0.5\text{ mm}$$

The pitch is precisely $$0.5\text{ mm}$$, which corresponds directly to Option (3).

When an external deforming force is applied to a body, an internal restoring force per unit cross-sectional area arises to oppose deformation: $$\text{Stress} = \frac{\text{Restoring Force}}{\text{Area}} = \frac{F}{A}$$.

- From Newton's second law $$F = ma$$: $$[F] = [\text{M}] \times [\text{L T}^{-2}] = [\text{M L T}^{-2}]$$ - Area is length squared: $$[A] = [\text{L}] \times [\text{L}] = [\text{L}^2]$$.

$$[\text{Stress}] = \frac{[F]}{[A]} = \frac{[\text{M L T}^{-2}]}{[\text{L}^2]} = [\text{M L}^{1 - 2}\text{T}^{-2}] = [\text{M L}^{-1}\text{T}^{-2}]$$.

Stress has identical dimensions to: - Pressure ($$P = F/A$$) - Young's modulus ($$Y$$ - Bulk modulus ($$B$$ - Modulus of rigidity ($$\eta$$ - Energy density ($$\text{Energy}/\text{Volume}$$ Matches Option 4.

For addition and subtraction of experimental measurements: 'The final result should retain as many decimal places as there are in the number with the least decimal places.'

- In $$9.99\text{ m}$$, there are 2 digits after the decimal point. - In $$0.0099\text{ m}$$, there are 4 digits after the decimal point. The result must therefore be restricted to 2 decimal places.

$$9.9900 - 0.0099 = 9.9801\text{ m}$$.

Looking at the third decimal digit in $$9.9801$$: it is $$0$$ ($$< 5$$), so the preceding digit ($$8$$) remains unaltered. Rounded result = $$9.98\text{ m}$$. Matches Option 2.