Units and Measurements Previous Year Questions — JEE Main Physics
50 past-year Units and Measurements questions from JEE Main (Physics) — page 4.
Q908 (2025)
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{P}\mathrm{L}^{Q}\mathrm{T}^{R}\mathrm{A}^{S}$, where value of '$Q$' and '$R$' are
- $(3, -5)$
- $(-2, 2)$
- $(-2, 1)$
- $(1, -1)$
### Related Formula
Ratio formulation:
$$\frac{\phi_E}{\phi_M} = \frac{E \cdot A}{B \cdot A} = \frac{E}{B}$$
From Maxwell's electromagnetic wave equations:
$$E = c \cdot B \implies \frac{E}{B} = c$$
where $c$ is the speed of light.
### Core Logic
Since the ratio reduces to the dimension of speed ($c$):
$$\left[\frac{\phi_E}{\phi_M}\right] = [c] = \mathrm{M}^0 \mathrm{L}^1 \mathrm{T}^{-1} \mathrm{A}^0$$
### Step 1: Identify Exponent Values
Matching indices with $\mathrm{M}^{P}\mathrm{L}^{Q}\mathrm{T}^{R}\mathrm{A}^{S}$:
* $P = 0$
* $Q = 1$
* $R = -1$
* $S = 0$
Hence, $(Q, R) = (1, -1)$.
### Pattern Recognition
Flux areas cancel out immediately. The ratio $\frac{E}{B}$ always carries the dimension of velocity ($\mathrm{L}\mathrm{T}^{-1}$).
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Units and Measurements
Class 12 Physics: Electromagnetic Waves
Q12 (2025)
Match List-I with List-II.
<div style="overflow-x: auto; margin: 1rem 0;"><table style="width: 100%; border-collapse: collapse; text-align: left; font-size: 14px;"><thead><tr><th style="border: 1px solid #888; padding: 8px;">List-I</th><th style="border: 1px solid #888; padding: 8px;">List-II</th></tr></thead><tbody><tr><td style="border: 1px solid #888; padding: 8px;">(A) Mass density</td><td style="border: 1px solid #888; padding: 8px;">(I) $[ML^{2}T^{-3}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(B) Impulse</td><td style="border: 1px solid #888; padding: 8px;">(II) $[MLT^{-1}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(C) Power</td><td style="border: 1px solid #888; padding: 8px;">(III) $[ML^{2}T^{0}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(D) Moment of inertia</td><td style="border: 1px solid #888; padding: 8px;">(IV) $[ML^{-3}T^{0}]$</td></tr></tbody></table></div>
Choose the correct answer from the options given below: [cite: 107]
- (A)-(IV), (B)-(II), (C)-(III), (D)-(I) [cite: 108]
- (A)-(I), (B)-(III), (C)-(IV), (D)-(II) [cite: 109]
- (A)-(IV), (B)-(II), (C)-(I), (D)-(III) [cite: 110]
- (A)-(II), (B)-(III), (C)-(IV), (D)-(I) [cite: 111]
### Core Logic
Let's derive the dimensional formulas systematically:
* **(A) Mass density:** $\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{M}{L^3} = [M^1 L^{-3} T^0] \implies \text{(IV)}$ [cite: 765].
* **(B) Impulse:** $I = F \cdot \Delta t = [M^1 L^1 T^{-2}] \cdot [T] = [M^1 L^1 T^{-1}] \implies \text{(II)}$ [cite: 767].
* **(C) Power:** $P = \frac{\text{Work}}{\text{Time}} = \frac{[M^1 L^2 T^{-2}]}{[T]} = [M^1 L^2 T^{-3}] \implies \text{(I)}$ [cite: 770].
* **(D) Moment of inertia:** $I = M r^2 = [M^1 L^2 T^0] \implies \text{(III)}$ [cite: 772].
Matching all four pairings establishes the layout: (A)-(IV), (B)-(II), (C)-(I), (D)-(III)[cite: 110, 758].
### Pattern Recognition
Isolating the unique matching option for a straightforward parameter like Mass Density (A-IV) or Moment of Inertia (D-III) easily allows exclusion of multiple invalid answer branches instantly[cite: 765, 772].
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Units and Measurements
Q1147 (2025)
The least count of a screw guage is $0.01 \mathrm{~mm}$ . If the pitch is increased by $75 \%$ and number of divisions on the circular scale is reduced by $50 \%$ , the new least count will be $\_ \times 10^{-3} \mathrm{~mm}$ .
### Related Formula
The Least Count (LC) of a screw gauge tool is defined by:
$$\text{L.C.} = \frac{\text{Pitch}}{\text{Total Number of Circular Divisions (N)}}$$
### Core Logic
The initial least count is given as:
$$\text{L.C.}_{\text{initial}} = \frac{P}{N} = 0.01\text{ mm}$$
Now, calculate the modified parameters from the text details :
* New Pitch: $P' = P(1 + 0.75) = 1.75P$
* New Divisions: $N' = N(1 - 0.50) = 0.5N$
### Step 1: Calculating the New Least Count
Set up the updated least count expression ratio :
$$\text{L.C.}_{\text{new}} = \frac{P'}{N'} = \frac{1.75P}{0.5N} = 3.5 \times \left(\frac{P}{N}\right)$$
Substitute the initial least count value :
$$\text{L.C.}_{\text{new}} = 3.5 \times 0.01\text{ mm} = 0.035\text{ mm}$$
Converting into the requested scientific prefix units ($10^{-3}\text{ mm}$) :
$$\text{L.C.}_{\text{new}} = 35 \times 10^{-3}\text{ mm}$$
Therefore, the requested value is 35.
### Pattern Recognition
Least count scales proportionally with pitch increases, and inversely with reductions in circular divisions.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Units and Measurements
Q4 (2025)
For an experimental expression $y=\frac{32.3\times1125}{27.4}$ , where all the digits are significant. Then to report the value of y we should write :-
- $y=1326.2$
- $y=1326.19$
- $y=1326.186$
- $y=1330$
### Related Formula
In multiplication and division arithmetic rules, the final product or quotient must be rounded off to retain as many significant figures as are present in the least precise operand.
### Core Logic
Let us check the significant digit count of the operands in the expression :
* $32.3$ has $3$ significant figures.
* $1125$ has $4$ significant figures.
* $27.4$ has $3$ significant figures.
The minimum number of significant figures among the numbers is $3$.
### Step 1: Rounding Off
Direct calculation yield :
$y = 1326.186...$
Rounding this value off to contain exactly 3 significant figures means changing it to 1330, since the digit after 2 is 6 (which is greater than 5), updating the hundreds spot upwards.
### Pattern Recognition
Never keep unearned precision from automated calculation. The output is bounded strictly by your least precise entry.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Units and Measurements
Q3 (2025)
Match List-I with List-II:
<div style="overflow-x: auto; margin: 1rem 0;"><table style="width: 100%; border-collapse: collapse; text-align: left; font-size: 14px;"><thead><tr><th style="border: 1px solid #888; padding: 8px;">List-I</th><th style="border: 1px solid #888; padding: 8px;">List-II</th></tr></thead><tbody><tr><td style="border: 1px solid #888; padding: 8px;">(A) Angular Impulse</td><td style="border: 1px solid #888; padding: 8px;">(I) $[M^{0}L^{2}T^{-2}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(B) Latent Heat</td><td style="border: 1px solid #888; padding: 8px;">(II) $[M L^{2}T^{-3}A^{-1}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(C) Electrical resistivity</td><td style="border: 1px solid #888; padding: 8px;">(III) $[M L^{2}T^{-1}]$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">(D) Electromotive force</td><td style="border: 1px solid #888; padding: 8px;">(IV) $[M L^{3}T^{-3"}A^{-2}]$</td></tr></tbody></table></div>
Choose the correct answer from the options given below:
- $\text{(A)-(III), (B)-(I), (C)-(IV), (D)-(II)}$
- $\text{(A)-(I), (B)-(III), (C)-(IV), (D)-(II)}$
- $\text{(A)-(III), (B)-(I), (C)-(II), (D)-(IV)}$
- $\text{(A)-(II), (B)-(I), (C)-(IV), (D)-(III)}$
### Related Formula
* **Angular Impulse** = Change in Angular Momentum = $\tau \cdot \Delta t = [M L^2 T^{-2}] \cdot [T] = [M L^2 T^{-1}]$ [cite: 670, 672]
* **Latent Heat** ($L$) = $\frac{Q}{m} = \frac{[M L^2 T^{-2}]}{[M]} = [M^0 L^2 T^{-2}]$
* **Electrical resistivity** (\rho) = $\frac{R \cdot A}{l} = \frac{[M L^2 T^{-3} A^{-2}] \cdot [L^2]}{[L]} = [M L^3 T^{-3} A^{-2}]$
* **Electromotive force** ($V$) = $\frac{W}{q} = \frac{[M L^2 T^{-2}]}{[A T]} = [M L^2 T^{-3} A^{-1}]$
### Core Logic
By comparing the formulas derived for each physical quantity with the options given in List-II [cite: 670, 673, 674]:
* (A) matches with (III) [cite: 670, 672]
* (B) matches with (I)
* (C) matches with (IV)
* (D) matches with (II)
Hence, the correct matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).
### Pattern Recognition
In match-the-column dimensional analysis questions, identifying even one or two straightforward quantities like Latent Heat ($L = Q/m$) often immediately eliminates three incorrect options, securing a quick correct answer.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 11 Physics: Units and Measurements
