physics : class11 Dimensional Consistency : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Dimensional Consistency
MCQ questions and answers.
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MCQ Questions
1. Which of the following equations is dimensionally consistent?
A.
s = ut + 1/2 at^2
B.
s = u + at^2
C.
s = ut^2 + 1/2 at
D.
s = u/t + at^2
Correct Answer:
s = ut + 1/2 at^2
Explanation:
The dimensions of ut are [L], and the dimensions of at^2 are also [L]. Therefore, both terms can be added to give displacement s, which has dimension [L].
2. For the equation x = a + bt, where x is displacement and t is time, what must be the dimension of b?
A.
[L]
B.
[T]
C.
[L T^-1]
D.
[L T]
Correct Answer:
[L T^-1]
Explanation:
Since a and x have the dimension [L], the term bt must also have dimension [L]. Thus, [b][T] = [L], so [b] = [L T^-1].
3. Which expression is dimensionally valid for adding to a quantity having the dimensions of velocity?
A.
Acceleration
B.
Displacement
C.
Speed
D.
Force
Correct Answer:
Speed
Explanation:
Quantities can be added only when they have the same dimensions. Speed and velocity both have dimensions [L T^-1].
4. In the equation y = A sin(ωt), what must be the dimension of ω for dimensional consistency?
A.
[T]
B.
[T^-1]
C.
[L T^-1]
D.
[L T^-2]
Correct Answer:
[T^-1]
Explanation:
The argument of a sine function must be dimensionless. Therefore, ωt must have no dimensions. Since [t] = [T], [ω] must be [T^-1].
5. Which equation is dimensionally inconsistent?
A.
v = u + at
B.
p = mv
C.
F = ma
D.
v = u + at^2
Correct Answer:
v = u + at^2
Explanation:
Velocity v and u have dimensions [L T^-1], while at^2 has dimensions [L]. Quantities with different dimensions cannot be added, so the equation is dimensionally inconsistent.
6. In the equation E = mc^2, which quantity has the same dimensions as E?
A.
mc
B.
mc^2
C.
m/c^2
D.
c^2/m
Correct Answer:
mc^2
Explanation:
Mass m has dimensions [M] and the square of speed c^2 has dimensions [L^2 T^-2]. Therefore, mc^2 has dimensions [M L^2 T^-2], the same as energy E.
7. For the equation v^2 = u^2 + 2as, which pair of terms can be added dimensionally?
A.
v and u^2
B.
v^2 and u^2
C.
u and as
D.
v and as
Correct Answer:
v^2 and u^2
Explanation:
Both v^2 and u^2 have dimensions [L^2 T^-2]. Also, as has the same dimensions, making the equation dimensionally consistent.
8. A physical equation contains the term log(kt). What must be the dimension of k for the equation to be dimensionally consistent?
A.
[T]
B.
[T^-1]
C.
[L T^-1]
D.
Dimensionless
Correct Answer:
[T^-1]
Explanation:
The argument of a logarithm must be dimensionless. Since kt must be dimensionless and [t] = [T], k must have dimensions [T^-1].
9. Which of the following equations is dimensionally consistent for pressure P?
A.
P = F/A
B.
P = FA
C.
P = F/A^2
D.
P = A/F
Correct Answer:
P = F/A
Explanation:
Pressure is force per unit area. The dimensions of F/A are [M L T^-2]/[L^2] = [M L^-1 T^-2], which are the dimensions of pressure.
10. In the equation Q = a + bt + ct^2, if Q represents length, what must be the dimension of c?
A.
[L]
B.
[L T^-1]
C.
[L T^-2]
D.
[L T^2]
Correct Answer:
[L T^-2]
Explanation:
Every term added to Q must have dimensions [L]. For ct^2 to have dimension [L], [c][T^2] = [L]. Hence, [c] = [L T^-2].
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