physics : class11 Derived Physical Dimensions : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
Practice important
Derived Physical Dimensions
MCQ questions and answers.
Page 1
of
1
|
10
MCQ Questions
1. A physical quantity X is defined as X = (pressure × area)/(density × speed²). What is the dimensional formula of X?
A.
[L²]
B.
[L]
C.
[T⁻²]
D.
[M L² T⁻²]
Correct Answer:
[L²]
Explanation:
Pressure has dimensions [M L⁻¹ T⁻²], area has [L²], density has [M L⁻³], and speed² has [L² T⁻²]. Therefore, X = [M L T⁻²]/[M L⁻¹ T⁻²] = [L²].
2. The quantity P is defined by P = √(pressure/density). What are the dimensions of P?
A.
[L T⁻¹]
B.
[L² T⁻²]
C.
[M⁻¹ L² T⁻²]
D.
[M L⁻¹ T⁻¹]
Correct Answer:
[L T⁻¹]
Explanation:
Pressure has dimensions [M L⁻¹ T⁻²] and density has [M L⁻³]. Their ratio is [L² T⁻²]. Taking the square root gives [L T⁻¹], the dimensions of speed.
3. In the relation F = 6πηrv, where F is force, r is length, and v is speed, what are the dimensions of the coefficient η?
A.
[M L⁻¹ T⁻¹]
B.
[M L T⁻¹]
C.
[M L⁻² T⁻¹]
D.
[M L⁻¹ T⁻²]
Correct Answer:
[M L⁻¹ T⁻¹]
Explanation:
Ignoring the dimensionless numerical factor, η = F/(rv). Thus, η = [M L T⁻²]/([L][L T⁻¹]) = [M L⁻¹ T⁻¹].
4. If the energy stored in a stretched system is given by E = kx², where x is displacement, what is the dimensional formula of k?
A.
[M T⁻²]
B.
[M L T⁻²]
C.
[M L⁻¹ T⁻²]
D.
[M L² T⁻²]
Correct Answer:
[M T⁻²]
Explanation:
The dimensions of energy are [M L² T⁻²]. Since k = E/x² and x² has dimensions [L²], k has dimensions [M T⁻²].
5. What are the dimensions of the product Gρ, where G is the universal gravitational constant and ρ is mass density?
A.
[T⁻²]
B.
[L T⁻²]
C.
[M T⁻²]
D.
[M⁻¹ L³ T⁻²]
Correct Answer:
[T⁻²]
Explanation:
The gravitational constant has dimensions [M⁻¹ L³ T⁻²], while density has [M L⁻³]. Their product is [T⁻²].
6. Surface tension is defined as force per unit length. Which dimensional formula represents surface tension?
A.
[M T⁻²]
B.
[M L T⁻²]
C.
[M L⁻¹ T⁻²]
D.
[M L² T⁻²]
Correct Answer:
[M T⁻²]
Explanation:
Force has dimensions [M L T⁻²]. Dividing by length [L] gives the dimensions of surface tension as [M T⁻²].
7. The quantity Q is defined as Q = ℏ/(mc), where ℏ is reduced Planck's constant, m is mass, and c is speed. What are the dimensions of Q?
A.
[L]
B.
[L² T⁻¹]
C.
[M L]
D.
[T]
Correct Answer:
[L]
Explanation:
Reduced Planck's constant has dimensions of angular momentum, [M L² T⁻¹]. The denominator mc has dimensions [M L T⁻¹]. Therefore, Q has dimensions [L].
8. A quantity Z is defined as Z = (momentum × length)/(energy × time). What is the dimensional formula of Z?
A.
[1]
B.
[T⁻¹]
C.
[L T⁻¹]
D.
[M L² T⁻²]
Correct Answer:
[1]
Explanation:
Momentum × length has dimensions [M L T⁻¹][L] = [M L² T⁻¹]. Energy × time has dimensions [M L² T⁻²][T] = [M L² T⁻¹]. Their ratio is dimensionless, represented by [1].
9. For a quantity R = √(energy/mass), what are its dimensions?
A.
[L T⁻¹]
B.
[L² T⁻¹]
C.
[M¹ᐟ² L T⁻¹]
D.
[L T⁻²]
Correct Answer:
[L T⁻¹]
Explanation:
Energy divided by mass has dimensions [M L² T⁻²]/[M] = [L² T⁻²]. Taking the square root gives [L T⁻¹].
10. The quantity C is defined by C = (force × time²)/(mass × length). What are the dimensions of C?
A.
[1]
B.
[T]
C.
[L]
D.
[M L T⁻²]
Correct Answer:
[1]
Explanation:
Force × time² has dimensions [M L T⁻²][T²] = [M L]. Mass × length also has dimensions [M L]. Hence, C is dimensionless and has dimensional formula [1].
Short Questions and Answers
Practice short questions and answers related to
Derived Physical Dimensions
.
Short questions are currently unavailable for this page.