A tiny metallic rectangular sheet has length and breadth of 5 ~mm$5 \mathrm{~mm}$ and 2.5 ~mm$2.5 \mathrm{~mm}$ , respectively. Using a specially designed screw gauge which has pitch of 0.75 ~mm$0.75 \mathrm{~mm}$ and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be x100$\frac{\mathrm{x}}{100}$ where x$\mathrm{x}$ is ________.

Related Formula

Significant Figures Rule for Addition/Subtraction: The final result must be rounded off to keep only as many decimal places as there are in the measurement with the least number of decimal places.

Core Logic

Let's look at the decimal places of each measurement:

• 435.42~g$435.42\mathrm{~g}$ has 2 decimal places.
• 226.3~g$226.3\mathrm{~g}$ has 1 decimal place.
• 0.125~g$0.125\mathrm{~g}$ has 3 decimal places.

The minimum number of decimal places is 1 decimal place (from 226.3~g$226.3\mathrm{~g}$).

Step 1: Addition and Rounding

First, perform the standard mathematical addition:

Now, round this raw sum off to 1 decimal place:

• The digit after tenths place is 4 (4 < 5$4 < 5$), so we round down.
• Net rounded sum = 661.8~g$661.8\mathrm{~g}$.

Pattern Recognition

Bust the common myth: Addition depends on the least number of decimal places, whereas multiplication/division depends on the least number of significant figures. Always distinguish between these two rules during exams!

Chapter Mix

Class 11 Physics: Units and Measurements: Error Analysis and Significant Figures

Related Formula

Core Logic

Statement I: Comparing the dimensional formula of Planck's constant (h$h$) and angular momentum (L$L$), both are identical [ML²T⁻¹]$[\text{M}\text{L}^2\text{T}^{-1}]$. Hence, Statement I is correct.

Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of (h)/(2π)$\frac{h}{2\pi}$, not an integral multiple of h$h$. Hence, Statement II is incorrect.

Pattern Recognition

Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of = (h)/(2π)$\hbar = \frac{h}{2\pi}$, making statement II a classic trap.

Chapter Mix

Class 11 Physics: Units and Measurements Class 12 Physics: Atoms

Related Formula

Core Logic

Calculate the value of one main scale division:

Given that 25 VSD = 24 MSD$25\text{ VSD} = 24\text{ MSD}$, we find:

Step 1: Compute Least Count

Pattern Recognition

Least count calculation is conventionally LC = 1 MSDN$\text{LC} = \frac{1\text{ MSD}}{N}$ where N$N$ represents the total count of divisions on the vernier scale whenever (N-1) MSD = N VSD$(N-1)\text{ MSD} = N\text{ VSD}$.

Chapter Mix

Class 11 Physics: Units and Measurements

Related Formula

Electric Dipole Moment: Pₑ = q · d [Pₑ] = A$P_e = q \cdot d \implies [P_e] = \text{A}\cdot\text{T}\cdot\text{L}$ Magnetic Dipole Moment: Mm = I · A [Mm] = A ²$M_m = I \cdot A \implies [M_m] = \text{A}\cdot\text{L}^2$

Core Logic

Take the dimensional ratio:

Comparing powers with [M^PL^QT^RA^S]$[\text{M}^P\text{L}^Q\text{T}^R\text{A}^S]$, we find: P = 0$P = 0$ Q = -1$Q = -1$

Pattern Recognition

Dipole units match up with fundamental currents and charge definitions. Notice that current A$A$ cancels out completely, leaving a simple geometric spatial ratio.

Chapter Mix

Class 11 Physics: Units and Measurements Class 12 Physics: Moving Charges and Magnetism

Related Formula

Ratio formulation:

From Maxwell's electromagnetic wave equations:

where c$c$ is the speed of light.

Core Logic

Since the ratio reduces to the dimension of speed (c$c$):

Step 1: Identify Exponent Values

Matching indices with MPLQTRAS$\mathrm{M}^{P}\mathrm{L}^{Q}\mathrm{T}^{R}\mathrm{A}^{S}$:

• P = 0$P = 0$
• Q = 1$Q = 1$
• R = -1$R = -1$
• S = 0$S = 0$

Hence, (Q, R) = (1, -1)$(Q, R) = (1, -1)$.

Pattern Recognition

Flux areas cancel out immediately. The ratio (E)/(B)$\frac{E}{B}$ always carries the dimension of velocity (LT⁻¹$\mathrm{L}\mathrm{T}^{-1}$).

Chapter Mix

Class 11 Physics: Units and Measurements Class 12 Physics: Electromagnetic Waves