Question:
If the dimension of (Angle × Force × Length) is \(M^{a}L^{b}T^{c}\) then the value of \((a,b,c)\) is:
If the dimension of (Angle × Force × Length) is \(M^{a}L^{b}T^{c}\) then the value of \((a,b,c)\) is:
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Angle is always dimensionless in physics.
Updated On: Jun 20, 2026
- (1, 1, -1)
- (1, 2, -2)
- (1, 1, 1)
- (1, 2, 2)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding dimensional analysis basics.
Every physical quantity can be expressed in terms of fundamental dimensions: mass (M), length (L), and time (T). To find the final dimension, each component must be analyzed separately and then multiplied.
Step 2: Dimension of angle.
Angle is a dimensionless quantity because it is the ratio of arc length to radius. Therefore, its dimensional formula is \(M^{0}L^{0}T^{0}\).
Step 3: Dimension of force.
Force is defined by Newton’s second law: \(F = mass \times acceleration\). Hence, its dimension is \(M^{1}L^{1}T^{-2}\).
Step 4: Dimension of length.
Length is a fundamental quantity with dimension \(L^{1}\). It contributes only to the power of L.
Step 5: Multiply all quantities.
(Angle × Force × Length) = \( (1) \times (M^{1}L^{1}T^{-2}) \times (L^{1}) \).
So combined dimension becomes \(M^{1}L^{2}T^{-2}\).
Step 6: Extract powers.
Comparing with \(M^{a}L^{b}T^{c}\), we get \(a=1, b=2, c=-2\).
Step 7: Final conclusion.
Thus, correct answer is (1, 2, -2).
Every physical quantity can be expressed in terms of fundamental dimensions: mass (M), length (L), and time (T). To find the final dimension, each component must be analyzed separately and then multiplied.
Step 2: Dimension of angle.
Angle is a dimensionless quantity because it is the ratio of arc length to radius. Therefore, its dimensional formula is \(M^{0}L^{0}T^{0}\).
Step 3: Dimension of force.
Force is defined by Newton’s second law: \(F = mass \times acceleration\). Hence, its dimension is \(M^{1}L^{1}T^{-2}\).
Step 4: Dimension of length.
Length is a fundamental quantity with dimension \(L^{1}\). It contributes only to the power of L.
Step 5: Multiply all quantities.
(Angle × Force × Length) = \( (1) \times (M^{1}L^{1}T^{-2}) \times (L^{1}) \).
So combined dimension becomes \(M^{1}L^{2}T^{-2}\).
Step 6: Extract powers.
Comparing with \(M^{a}L^{b}T^{c}\), we get \(a=1, b=2, c=-2\).
Step 7: Final conclusion.
Thus, correct answer is (1, 2, -2).
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