1. What is the dimensional formula of velocity?
A.
[M L T^-1]
B.
[M^0 L T^-1]
C.
[M^0 L T^-2]
D.
[M L^0 T^-1]
Correct Answer:
[M^0 L T^-1]
Explanation:
Velocity is displacement divided by time. Therefore, its dimensions are [L]/[T] = [M^0 L T^-1].
2. Which of the following equations is dimensionally correct?
A.
s = u + at^2
B.
s = ut + (1/2)at^2
C.
s = u/t + at
D.
s = ut^2 + (1/2)at
Correct Answer:
s = ut + (1/2)at^2
Explanation:
In this equation, ut and at^2 both have the dimensions of length, so they can be added to give displacement s.
3. The equation F = Gm1m2/r^2 is used to define the gravitational constant G. What are the dimensions of G?
A.
[M^-1 L^3 T^-2]
B.
[M L^3 T^-2]
C.
[M^-1 L^2 T^-2]
D.
[M L^-1 T^-2]
Correct Answer:
[M^-1 L^3 T^-2]
Explanation:
From G = Fr^2/(m1m2), the dimensions are [M L T^-2][L^2]/[M^2] = [M^-1 L^3 T^-2].
4. Which equation is dimensionally homogeneous?
A.
v = u + at
B.
v = u + at^2
C.
v^2 = u^2 + at
D.
v = u^2 + at
Correct Answer:
v = u + at
Explanation:
The quantities v, u, and at all have dimensions of velocity, [L T^-1]. Hence, the equation is dimensionally homogeneous.
5. If force F is related to displacement x by F = kx, what are the dimensions of k?
A.
[M L T^-2]
B.
[M T^-2]
C.
[M L^-1 T^-2]
D.
[M^-1 T^2]
Correct Answer:
[M T^-2]
Explanation:
From k = F/x, the dimensions of k are [M L T^-2]/[L] = [M T^-2].
6. The dimensional formula of pressure can be obtained from the equation P = F/A. What is it?
A.
[M L^-1 T^-2]
B.
[M L T^-2]
C.
[M L^-2 T^-1]
D.
[M^0 L^-1 T^-2]
Correct Answer:
[M L^-1 T^-2]
Explanation:
Pressure equals force divided by area. Thus, its dimensions are [M L T^-2]/[L^2] = [M L^-1 T^-2].
7. In the equation x = at^2, where x is displacement and t is time, what are the dimensions of a?
A.
[L T^-1]
B.
[L T^-2]
C.
[L^2 T^-2]
D.
[M L T^-2]
Correct Answer:
[L T^-2]
Explanation:
Since a = x/t^2, its dimensions are [L]/[T^2] = [L T^-2].
8. Which equation is dimensionally valid for kinetic energy?
A.
K = mv
B.
K = (1/2)mv^2
C.
K = (1/2)mv
D.
K = m/v^2
Correct Answer:
K = (1/2)mv^2
Explanation:
The dimensions of mv^2 are [M][L^2 T^-2] = [M L^2 T^-2], which are the dimensions of energy.
9. The equation E = mc^2 is dimensionally correct because both sides have the dimensions of:
A.
Force
B.
Power
C.
Energy
D.
Momentum
Correct Answer:
Energy
Explanation:
The dimensions of mc^2 are [M][L^2 T^-2] = [M L^2 T^-2], which are the dimensions of energy.
10. In the equation T = 2π√(l/g), where l is length and g is acceleration, the dimensions of the right-hand side are:
A.
[T]
B.
[L]
C.
[T^-1]
D.
[L T^-1]
Correct Answer:
[T]
Explanation:
The dimensions of l/g are [L]/[L T^-2] = [T^2]. Taking the square root gives [T], and 2π is dimensionless.
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