physics : class11 Dimensional Formula of Gravitational Force : Gravitational Force : Gravitation MCQ Questions and Answers
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Dimensional Formula of Gravitational Force
MCQ questions and answers.
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MCQ Questions
1. What is the dimensional formula of gravitational force?
A.
[M L T^-2]
B.
[M L^2 T^-2]
C.
[M^0 L T^-1]
D.
[M L^-1 T^-2]
Correct Answer:
[M L T^-2]
Explanation:
Gravitational force is a force, and force = mass × acceleration. Therefore, its dimensional formula is [M] × [L T^-2] = [M L T^-2].
2. Using Newton's second law, the dimensional formula of gravitational force is:
A.
[M L^2 T^-2]
B.
[M L T^-2]
C.
[M L^-1 T^-2]
D.
[M^0 L T^-2]
Correct Answer:
[M L T^-2]
Explanation:
From F = ma, mass has dimensions [M] and acceleration has dimensions [L T^-2]. Hence, force has dimensions [M L T^-2].
3. Which of the following represents the dimensional formula of gravitational force between two masses?
A.
[M^2 L T^-2]
B.
[M L T^-1]
C.
[M L T^-2]
D.
[M L^2 T^-1]
Correct Answer:
[M L T^-2]
Explanation:
Although gravitational force is calculated using F = Gm1m2/r^2, the resulting physical quantity is force. Its dimensional formula is [M L T^-2].
4. The dimensions of gravitational force are the same as the dimensions of:
A.
Energy
B.
Momentum
C.
Power
D.
Force
Correct Answer:
Force
Explanation:
Gravitational force is itself a force, so its dimensional formula is [M L T^-2]. Energy, momentum, and power have different dimensional formulas.
5. If gravitational force F = mass × acceleration, what is its dimensional formula?
A.
[M L T^-2]
B.
[M L^2 T^-2]
C.
[M^0 L T^-2]
D.
[M L^-2 T^2]
Correct Answer:
[M L T^-2]
Explanation:
Mass has dimensional formula [M], while acceleration has dimensional formula [L T^-2]. Their product gives [M L T^-2].
6. Which powers of M, L, and T occur in the dimensional formula [M^a L^b T^c] for gravitational force?
A.
a = 1, b = 1, c = -2
B.
a = 1, b = 2, c = -2
C.
a = 0, b = 1, c = -1
D.
a = 2, b = -1, c = -2
Correct Answer:
a = 1, b = 1, c = -2
Explanation:
The dimensional formula of force is [M L T^-2]. Therefore, the powers are a = 1, b = 1, and c = -2.
7. The dimensional formula of gravitational force is obtained from which relation?
A.
F = mv
B.
F = ma
C.
F = m/v
D.
F = m/a
Correct Answer:
F = ma
Explanation:
Newton's second law gives F = ma. Substituting the dimensions of mass and acceleration gives the gravitational force dimensions [M L T^-2].
8. What is the time dimension in the dimensional formula of gravitational force?
A.
T
B.
T^2
C.
T^-1
D.
T^-2
Correct Answer:
T^-2
Explanation:
Gravitational force has the dimensional formula [M L T^-2], so the power of time is -2.
9. What is the mass dimension in the dimensional formula of gravitational force?
A.
M^0
B.
M^-1
C.
M
D.
M^2
Correct Answer:
M
Explanation:
Since force equals mass multiplied by acceleration, the mass dimension in gravitational force is M^1, written as M.
10. What is the length dimension in the dimensional formula of gravitational force?
A.
L^-1
B.
L
C.
L^2
D.
L^0
Correct Answer:
L
Explanation:
Acceleration has the length dimension L, and force is mass multiplied by acceleration. Therefore, gravitational force has length dimension L^1.
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