Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below:

Statement I: Comparing the dimensional formula of Planck's constant (h) and angular momentum (L), both are identical [ML2T-1]. Hence, Statement I is correct. Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of (h/2pi), not an integral multiple of h. Hence, Statement II is incorrect. Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of = (h/2pi), making statement II a classic trap. Class 11 Physics: Units and Measurements Class 12 Physics: Atoms

Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbi

Statement I: Comparing the dimensional formula of Planck's constant (h) and angular momentum (L), both are identical [ML2T-1]. Hence, Statement I is correct. Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of (h/2pi), not an integral multiple of h. Hence, Statement II is incorrect. Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of = (h/2pi), making statement II a classic trap. Cl

Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below:

Statement I: Comparing the dimensional formula of Planck's constant (h) and angular momentum (L), both are identical [ML2T-1]. Hence, Statement I is correct. Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of (h/2pi), not an integral multiple of h. Hence, Statement II is incorrect. Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of = (h/2pi), making statement II a classic trap. Class 11 Physics: Units and Measurements Class 12 Physics: Atoms

Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II): In Bohr's model electron revolve around the nucleus only in those orbi

Statement I: Comparing the dimensional formula of Planck's constant (h) and angular momentum (L), both are identical [ML2T-1]. Hence, Statement I is correct. Statement II: According to Bohr's second postulate, angular momentum is an integral multiple of (h/2pi), not an integral multiple of h. Hence, Statement II is incorrect. Watch out for exact definitions in standard postulates. Bohr's model requires angular momentum to be quantized in units of = (h/2pi), making statement II a classic trap. Cl

Given below are two statements: Statement (I): The dimensions of Planck's constant and angular momentum are same…

Year	2026	2025	2024	Total
Questions	14	22	14	50

Q16 jee_main_2025_29_jan_evening Dimensional Analysis

Match List-I with List-II.

array|l|l|l|l| List-I & & List-II & (A) & Young's Modulus & (I) & ML⁻¹T⁻¹ (B) & Torque & (II) & ML⁻¹T⁻² (C) & Coefficient of Viscosity & (III) & M⁻¹L³T⁻² (D) & Gravitational Constant & (IV) & ML²T⁻² array

Choose the correct answer from the options given below:

A. $(A)-(I), (B)-(III), (C)-(II), (D)-(IV)$
B. $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$
C. $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
D. $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$

Solution

Related Formula

Young's Modulus: Y = (F/A)/(Δ / )

Torque: τ = F \cdot r

Viscosity Force: F = η A (dv)/(dx)

Gravitational Force: F = (G m₁ m₂)/(r²)

Core Logic

Evaluating dimensions component-by-component:

(A) Young's Modulus:

[Y] = ([F])/([A]) = MLT⁻²L² = ML⁻¹T⁻² arrow (II)

(B) Torque:

[τ] = [F][r] = ( MLT⁻²)(L) = ML²T⁻² arrow (IV)

(C) Coefficient of Viscosity:

[η] = ([F])/([A][dv/dx]) = MLT⁻²(L²)( T⁻¹) = ML⁻¹T⁻¹ arrow (I)

(D) Gravitational Constant:

[G] = ([F][r²])/([m₁][m₂]) = ( MLT⁻²)(L²)M² = M⁻¹L³T⁻² arrow (III)

Matching path yields: (A)-(II), (B)-(IV), (C)-(I), (D)-(III).

Pattern Recognition

Torque and energy share the identical dimensional formula $ML²T⁻²$ $\mathrm{ML^2T^{-2}}$. Modulus and pressure share $ML⁻¹T⁻²$ $\mathrm{ML^{-1}T^{-2}}$. Spotting these matching associations cuts solving time significantly.

Chapter Mix

Class 11 Physics: Units and Measurements

Q23 jee_main_2025_29_jan_evening Combination of Errors

A physical quantity

Q

is related to four observables

a, b, c, d

as follows:

Q = (ab⁴)/(cd)

where,

a = (60 \pm 3)~Pa

;

b = (20 \pm 0.1)~m

;

c = (40 \pm 0.2)~Nsm⁻²

and

d = (50 \pm 0.1)~m

, then the percentage error in

Q

is

(x)/(1000)

, where

x =

______.

Numerical Answer. Answer: 7700 to 7700

Solution

Related Formula

(Δ Q)/(Q) = (Δ a)/(a) + 4(Δ b)/(b) + (Δ c)/(c) + (Δ d)/(d)

Core Logic

Write down fractional errors from the raw text configurations:

$(Δ a)/(a) = (3)/(60) = 0.05$
$(Δ b)/(b) = (0.1)/(20) = 0.005$
$(Δ c)/(c) = (0.2)/(40) = 0.005$
$(Δ d)/(d) = (0.1)/(50) = 0.002$

Compute the total fractional error expression:

(Δ Q)/(Q) = [0.05 + 4(0.005) + 0.005 + 0.002]

(Δ Q)/(Q) = 0.05 + 0.02 + 0.005 + 0.002 = 0.077

Percentage error expression configuration:

% Error = (Δ Q)/(Q) \times 100 = 7.7 %

Given that percentage error equals $(x)/(1000)$ $\frac{x}{1000}$:

(x)/(1000) = 7.7 x = 7700

Pattern Recognition

Powers scale up error contributions via direct multiplication multipliers. The term $b⁴$ $b^4$ contributes exactly 4 times its basic fraction error component to the compilation step.

Chapter Mix

Class 11 Physics: Units and Measurements

Q21 jee_main_2025_28_jan_morning Errors in Measurement

A tiny metallic rectangular sheet has length and breadth of

5 ~mm

and

2.5 ~mm

, respectively. Using a specially designed screw gauge which has pitch of

0.75 ~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

where

x

is ________.

Numerical Answer. Answer: 3 to 3

Solution

Core Logic

First, find the least count of the measurement tool:

Least Count = PitchNumber of circular scale divisions = 0.75 ~mm15 = 0.05 ~mm

Least count calculation tracking diagram for Q21

The area of the rectangular metallic sheet is calculated as:

A = L \cdot W

Expressing the absolute error via fractional configuration parts:

dAA = dLL + dWW

Substituting the instrument limits ( $dL = dW = 0.05 ~mm$ ):

dAA = (0.05)/(5) + (0.05)/(2.5) = (1)/(100) + (2)/(100) = (3)/(100)

Step 1: Final Value Match

Comparing this to the target format $x100$ $\frac{\mathrm{x}}{100}$ gives:

$x = 3$ $\mathrm{x} = 3$

Pattern Recognition

The absolute measurement uncertainty matches the instrument's least count value directly. Sum up individual fractional errors to compute the total area uncertainty parameter.

Chapter Mix

Class 11 Physics: Units and Measurements

Q23 jee_main_2025_28_jan_morning Dimensional Analysis

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of

[MaLbTc]

. If

b = 3

, the value of

c

is

Numerical Answer. Answer: 0 to 0

Solution

Core Logic

Let's find the dimensional formula for the ratio of Modulus of Elasticity to Torque:

Target Dimensions = [Modulus of Elasticity][Torque]

Target Dimensions = [M L⁻¹ T⁻²][M L² T⁻²] = [M⁰ L⁻³ T⁰]

Step 1: Exponent Matching

Comparing this output to the target layout formula $[Ma Lb Tc]$ :

$c = 0$ $\mathrm{c} = 0$

Pattern Recognition

Both dimensions share identical time dependence factors ( $T⁻²$ $\mathrm{T}^{-2}$), meaning they cancel out completely. This leaves the time exponent value as exactly zero.

Chapter Mix

Class 11 Physics: Units and Measurements

Q9 jee_main_2025_03_april_morning Dimensional Formulae

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Gravitational constant	I. $[LT⁻²]$ $[LT^{-2}]$
B. Gravitational potential energy	II. $[L²T⁻²]$ $[L^2T^{-2}]$
C. Gravitational potential	III. $[ML²T⁻²]$ $[ML^2T^{-2}]$
D. Acceleration due to gravity	IV. $[M⁻¹L³T⁻²]$ $[M^{-1}L^3T^{-2}]$

Choose the correct answer from the options given below:

A. A-IV, B-III, C-II, D-I
B. A-III, B-II, C-I, D-IV
C. A-II, B-IV, C-III, D-I
D. A-I, B-III, C-IV, D-II

Solution

Related Formula

Newton's Law of Gravitation:

F = G(m₁ m₂)/(r²) G = (Fr²)/(m₁ m₂)

Potential Energy:

U = mgh [Work]

Potential:

V = (W)/(m)

Acceleration:

g = VelocityTime

Core Logic

Let's perform dimensional analysis for each item:

A. Gravitational constant ( $G$ $G$):

[G] = ([F][r²])/([M²]) = [MLT⁻²][L²][M²] = [M⁻¹L³T⁻²]

Matches with IV.

B. Gravitational potential energy ( $U$ $U$):

[U] = Dimensions of Work = [ML²T⁻²]

Matches with III.

C. Gravitational potential ( $V$ $V$):

[V] = [Energy][M] = [ML²T⁻²][M] = [L²T⁻²]

Matches with II.

D. Acceleration due to gravity ( $g$ $g$):

[g] = [Acceleration] = [LT⁻²]

Matches with I.

Step 1: Match and Selection

Let's align our matches:

A $arrow$ $\rightarrow$ IV
B $arrow$ $\rightarrow$ III
C $arrow$ $\rightarrow$ II
D $arrow$ $\rightarrow$ I

This sequence matches option (1).

Pattern Recognition

To save precious exam time on match-the-column questions, start with the easiest dimensional terms first. You know Acceleration due to gravity is $g arrow [LT⁻²]$ $g \rightarrow [LT^{-2}]$ (D-I) and energy is $[ML²T⁻²]$ $[ML^2T^{-2}]$ (B-III). Looking at the options, only Option 1 matches this sequence immediately!

Chapter Mix

Class 11 Physics: Units and Measurements Class 11 Physics: Gravitation

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