physics : class11 Dimensions of Coefficients : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Dimensions of Coefficients
MCQ questions and answers.
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MCQ Questions
1. A viscous force on a spherical body is given by F = 6π η r v, where r is radius and v is speed. What are the dimensions of the coefficient of viscosity η?
A.
M L^-1 T^-1
B.
M L T^-1
C.
M L^-1 T^-2
D.
M L T^-2
Correct Answer:
M L^-1 T^-1
Explanation:
Since F = ηrv apart from the dimensionless factor 6π, [η] = [F]/([r][v]) = (M L T^-2)/(L × L T^-1) = M L^-1 T^-1.
2. The resistive force acting on a body is expressed as F = a v + b v^2. What is the dimensional formula of the ratio a/b?
A.
L T^-1
B.
L^-1 T
C.
L T
D.
L^-1 T^-1
Correct Answer:
L T^-1
Explanation:
From av having the dimensions of force, [a] = [F]/[v] = M T^-1. From bv^2 having the dimensions of force, [b] = [F]/[v^2] = M L^-1. Therefore, [a/b] = (M T^-1)/(M L^-1) = L T^-1.
3. A displacement is represented by x = a t^2 + b t^3, where x is displacement and t is time. What is the dimensional formula of a/b?
A.
T
B.
T^-1
C.
L T
D.
L T^-1
Correct Answer:
T
Explanation:
Since [a t^2] = L, [a] = L T^-2. Similarly, [b t^3] = L gives [b] = L T^-3. Hence [a/b] = (L T^-2)/(L T^-3) = T.
4. A force depends on displacement according to F = kx + cx^2. What is the dimensional formula of k/c?
A.
L
B.
L^-1
C.
M L
D.
M^-1 L
Correct Answer:
L
Explanation:
For kx to represent force, [k] = [F]/[x] = M T^-2. For cx^2 to represent force, [c] = [F]/[x^2] = M L^-1 T^-2. Thus [k/c] = L.
5. The angular equation for a rotating body is τ = aθ + bω + cα, where θ is angular displacement, ω is angular velocity, and α is angular acceleration. What are the dimensions of a/(bc)?
A.
M^-1 L^-2 T^-1
B.
M^-1 L^-2 T
C.
M L^-2 T^-1
D.
M^-1 L^2 T^-1
Correct Answer:
M^-1 L^-2 T^-1
Explanation:
Torque has dimensions M L^2 T^-2. Since θ is dimensionless, [a] = M L^2 T^-2. Since [ω] = T^-1, [b] = M L^2 T^-1. Since [α] = T^-2, [c] = M L^2. Therefore, [a/(bc)] = (M L^2 T^-2)/[(M L^2 T^-1)(M L^2)] = M^-1 L^-2 T^-1.
6. A physical relation is written as v^2 = Ar + B/r, where v is velocity and r is length. What is the dimensional formula of AB?
A.
L^4 T^-4
B.
L^2 T^-4
C.
L^4 T^-2
D.
L^3 T^-4
Correct Answer:
L^4 T^-4
Explanation:
Since [v^2] = L^2 T^-2, from Ar we obtain [A] = L T^-2. From B/r we obtain [B] = L^3 T^-2. Hence [AB] = (L T^-2)(L^3 T^-2) = L^4 T^-4.
7. The energy stored in a deformed system is given by U = ax^2 + bx^3, where x is length. What is the dimensional formula of a/b?
A.
L
B.
L^-1
C.
M L
D.
M^-1 L
Correct Answer:
L
Explanation:
Energy has dimensions M L^2 T^-2. Thus [a] = [U]/L^2 = M T^-2, while [b] = [U]/L^3 = M L^-1 T^-2. Therefore, [a/b] = L.
8. A quantity Q varies with time according to Q = At + Bt^2 + C, where Q has dimensions of electric charge. What is the dimensional formula of B/A?
9. The pressure exerted by a fluid is modeled as P = aρv^2 + bρgh, where ρ is density, v is velocity, g is acceleration due to gravity, and h is height. What is the dimensional formula of a/b?
A.
1
B.
L
C.
T^-1
D.
M L^-1 T^-2
Correct Answer:
1
Explanation:
Both ρv^2 and ρgh have the dimensions of pressure. Therefore, both a and b must be dimensionless, so their ratio a/b is also dimensionless.
10. A damped oscillator is described by the equation m(d^2x/dt^2) + c(dx/dt) + kx = 0. What is the dimensional formula of k/c?
A.
T^-1
B.
T
C.
L T^-1
D.
M T^-1
Correct Answer:
T^-1
Explanation:
Each term has dimensions of force. From kx, [k] = M T^-2. From c(dx/dt), [c] = M T^-1. Hence [k/c] = (M T^-2)/(M T^-1) = T^-1.
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