A person measures mass of 3 different particles as 435.42~g$435.42\mathrm{~g}$, 226.3~g$226.3\mathrm{~g}$ and 0.125~g$0.125\mathrm{~g}$. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

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