Force = mass × acceleration, and acceleration has the dimensions [L T⁻²]. So the dimensional formula of force is [M L T⁻²].
A.
[M L T⁻¹] is the dimensional formula of momentum.
B.
[M L² T⁻²] is the dimensional formula of work or energy.
D.
[M L⁻¹ T⁻²] is the dimensional formula of pressure.
NCERT: Class 11 Physics, Chapter 1, 1.5
Sample 2Medium
The speed v of a transverse wave on a stretched string is assumed to depend only on the tension T in the string and its mass per unit length μ. Dimensional analysis shows that v is proportional to
A
√(T/μ)
B
√(μ/T)
C
T/μ
D
√(Tμ)
Show the answer
The answer is A.
T has dimensions [M L T⁻²] and μ has [M L⁻¹], so T/μ has [L² T⁻²]. Matching [L T⁻¹] requires v ∝ (T/μ)^½.
B.
√(μ/T) has dimensions [T L⁻¹], the inverse of a speed.
C.
T/μ has dimensions [L² T⁻²], the square of a speed.
D.
√(Tμ) has dimensions [M L⁰ T⁻¹], not [L T⁻¹].
NCERT: Class 11 Physics, Chapter 1, Dimensional analysis and its applications
Sample 3NEET level
Match List I (physical quantity) with List II (dimensional formula). List I: (A) Surface tension (B) Coefficient of viscosity (C) Impulse (D) Power List II: (I) [M L² T⁻³] (II) [M T⁻²] (III) [M L⁻¹ T⁻¹] (IV) [M L T⁻¹] Choose the correct answer.
A
A-II, B-IV, C-III, D-I
B
A-I, B-III, C-IV, D-II
C
A-II, B-III, C-IV, D-I
D
A-III, B-II, C-IV, D-I
Show the answer
The answer is C.
Surface tension is force per unit length, [M T⁻²]; viscosity coefficient is force/(area × velocity gradient), [M L⁻¹ T⁻¹]. Impulse is force × time, [M L T⁻¹], and power is work per unit time, [M L² T⁻³].
A.
Swaps viscosity and impulse: impulse is force × time, [M L T⁻¹], not [M L⁻¹ T⁻¹].
B.
Swaps surface tension and power: surface tension is force per length, [M T⁻²].
D.
Swaps surface tension and viscosity: surface tension has no length dimension.
NCERT: Class 11 Physics, Chapter 1 (Units and Measurements), Dimensions of physical quantities
Practise Dimensions of physical quantities and dimensional analysis
Practice at the level you choose, with the answer after every question; timed tests with the answers when you submit. Every question is verified against NCERT first.