If force [F] , acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy. - Physics MCQ NEET 2021 2026 | ExamTest.live | ExamTest.live

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If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

A $[F] [A] [T^{- 1}]$
B $[F] [A^{- 1}] [T]$
C $[F] [A] [T]$
D $[F] [A] [T^{2}]$

Solution & Step-by-step Explanation

Let Energy E \propto F^{a} A^{b} T^{c} .Dimension of Energy [E] = [M L^{2} T^{- 2}] Dimension of Force [F] = [M L T^{- 2}] Dimension of Acceleration [A] = [L T^{- 2}] Dimension of Time [T] = [T] Substituting in the equation: [M L^{2} T^{- 2}] = [M L T^{- 2}]^{a} [L T^{- 2}]^{b} [T]^{c} [M L^{2} T^{- 2}] = [M^{a} L^{a + b} T^{- 2 a - 2 b + c}] Comparing powers: a = 1 a + b = 2 \Rightarrow 1 + b = 2 \Rightarrow b = 1 - 2 a - 2 b + c = - 2 \Rightarrow - 2 (1) - 2 (1) + c = - 2 - 4 + c = - 2 \Rightarrow c = 2 The dimensions are [F] [A] [T^{2}] .

Practice this question

Try it yourself before checking the explanation above.

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

A

[F] [A] [T^{- 1}]

B

[F] [A^{- 1}] [T]

C

[F] [A] [T]

D

[F] [A] [T^{2}]

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