physics : class11 Principle of Homogeneity : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Principle of Homogeneity
MCQ questions and answers.
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MCQ Questions
1. According to the principle of homogeneity, which statement about a physical equation is correct?
A.
Only numerical values on both sides must be equal
B.
Dimensions of all terms in the equation must be the same
C.
Units of all quantities must be different
D.
Only the largest term needs to have correct dimensions
Correct Answer:
Dimensions of all terms in the equation must be the same
Explanation:
The principle of homogeneity states that every term in a physically meaningful equation must have the same dimensions.
2. Which of the following equations satisfies the principle of homogeneity?
A.
s = ut + 1/2 at^2
B.
s = u + at^2
C.
v = u + at^2
D.
F = mv
Correct Answer:
s = ut + 1/2 at^2
Explanation:
The dimensions of s, ut, and at^2 are all [L], so the equation is dimensionally homogeneous.
3. In the equation x = A + Bt, the dimensions of A must be the same as those of:
A.
B
B.
t
C.
x
D.
Bt only if t is dimensionless
Correct Answer:
x
Explanation:
Since A and Bt are added, both must have the same dimensions as x according to the principle of homogeneity.
4. Which equation is dimensionally invalid because unlike quantities are added?
A.
v = u + at
B.
s = ut + 1/2 at^2
C.
a = (v - u)/t
D.
v = u + at^2
Correct Answer:
v = u + at^2
Explanation:
The dimensions of v and u are [LT^-1], whereas at^2 has dimensions [L]. Therefore, the terms cannot be added.
5. If the equation y = a + bt is dimensionally homogeneous, which relation is correct?
A.
[a] = [b]
B.
[a] = [t]
C.
[a] = [y] and [bt] = [y]
D.
[b] = [y] and [a] = [t]
Correct Answer:
[a] = [y] and [bt] = [y]
Explanation:
Every term being added must have the same dimensions. Thus, a and bt must each have the dimensions of y.
6. The equation q = a + bt + ct^2 is homogeneous. What must be the dimensions of bt?
A.
The dimensions of a
B.
The dimensions of t
C.
The dimensions of c only
D.
Dimensionless in every case
Correct Answer:
The dimensions of a
Explanation:
Since a, bt, and ct^2 are added, all three terms must have identical dimensions. Therefore, bt has the same dimensions as a.
7. Which expression obeys the principle of homogeneity for displacement s, velocity u, acceleration a, and time t?
A.
s = ut + at
B.
s = u + at
C.
s = ut + 1/2 at^2
D.
s = u/t + at^2
Correct Answer:
s = ut + 1/2 at^2
Explanation:
Both ut and at^2 have dimensions of length, which are the dimensions of s. Hence, the equation is homogeneous.
8. In a homogeneous equation, why can two terms with different dimensions not be added?
A.
Their numerical values are always zero
B.
Addition is defined only for quantities of the same dimensions
C.
Their units must always be identical in name
D.
The equation would contain too many variables
Correct Answer:
Addition is defined only for quantities of the same dimensions
Explanation:
The principle of homogeneity requires terms being added or subtracted to have identical dimensions, making the equation physically meaningful.
9. For the equation v^2 = u^2 + 2as, which terms must have the same dimensions?
A.
Only v and u
B.
Only a and s
C.
v^2, u^2, and 2as
D.
v, u, and s
Correct Answer:
v^2, u^2, and 2as
Explanation:
The terms on both sides of an equation must have the same dimensions. Here, v^2, u^2, and 2as all have dimensions of velocity squared.
10. Which equation fails the principle of homogeneity?
A.
p = mv
B.
W = Fs
C.
E = mc^2
D.
p = m + v
Correct Answer:
p = m + v
Explanation:
Mass and velocity have different dimensions, so they cannot be added. Therefore, p = m + v is not dimensionally homogeneous.
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