physics : class11 Checking Physical Equations : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Checking Physical Equations
MCQ questions and answers.
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MCQ Questions
1. Which of the following equations is dimensionally correct?
A.
v = u + at
B.
v = u + at^2
C.
v = u^2 + at
D.
v^2 = u + at
Correct Answer:
v = u + at
Explanation:
Velocity v and initial velocity u have the same dimensions. The product at also has dimensions of velocity, so the equation is dimensionally correct.
2. Which of the following equations is dimensionally incorrect?
A.
s = ut + 1/2 at^2
B.
v^2 = u^2 + 2as
C.
s = ut + at
D.
p = mv
Correct Answer:
s = ut + at
Explanation:
The displacement s and ut have dimensions of length, but at has dimensions of velocity. Therefore, these terms cannot be added, making the equation dimensionally incorrect.
3. In the equation v = u + xt, where v and u are velocities and t is time, what are the dimensions of x?
A.
[L T^-2]
B.
[L T^-1]
C.
[L^2 T^-2]
D.
[T^-1]
Correct Answer:
[L T^-2]
Explanation:
Since xt must have the dimensions of velocity, x must have dimensions of velocity divided by time, which is [L T^-2].
4. Which equation passes the dimensional consistency test?
A.
F = ma
B.
F = mv
C.
F = m/a
D.
F = m + a
Correct Answer:
F = ma
Explanation:
Mass multiplied by acceleration has dimensions [M][L T^-2] = [M L T^-2], which are the dimensions of force.
5. Which of the following equations is dimensionally correct for energy?
A.
E = mc^2
B.
E = mc
C.
E = m/c^2
D.
E = m + c^2
Correct Answer:
E = mc^2
Explanation:
Mass multiplied by the square of speed has dimensions [M][L^2 T^-2], which are the dimensions of energy.
6. Which equation for the time period of a simple pendulum is dimensionally correct?
A.
T = 2π√(l/g)
B.
T = 2π√(g/l)
C.
T = 2π(lg)
D.
T = 2π(l/g)
Correct Answer:
T = 2π√(l/g)
Explanation:
The ratio l/g has dimensions [L]/[L T^-2] = [T^2]. Its square root has dimensions of time, so the equation is dimensionally correct.
7. What is necessary for two physical quantities to be added in a physical equation?
A.
They must have the same dimensions
B.
They must have different dimensions
C.
They must have the same numerical value
D.
They must have different units only
Correct Answer:
They must have the same dimensions
Explanation:
Terms that are added or subtracted in a physical equation must have identical dimensions for the equation to be dimensionally consistent.
8. Which of the following equations is dimensionally correct for pressure?
A.
P = F/A
B.
P = FA
C.
P = F + A
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.
9. Which equation is dimensionally incorrect?
A.
s = vt
B.
a = v/t
C.
p = mv
D.
s = v + t
Correct Answer:
s = v + t
Explanation:
Displacement has dimensions of length, while velocity and time have different dimensions. Therefore, v and t cannot be added in this equation.
10. Dimensional analysis can be used to check whether a physical equation is:
A.
Dimensionally consistent
B.
Numerically exact in every case
C.
Independent of all physical laws
D.
Correct only when units are omitted
Correct Answer:
Dimensionally consistent
Explanation:
Dimensional analysis verifies whether both sides of an equation have the same dimensions. It cannot by itself prove the complete numerical correctness of an equation.
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