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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]
- b)[F][A][T2]
- c)[F][A][T−1]
- d)[F][A−1][T]
Correct answer is option 'B'. Can you explain this answer?
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If force [F], acceleration [A] and time [T] are chosen as the fundame...
Dimensions of Energy:
Energy is defined as the capacity to do work or the ability to cause changes in a system. In the context of fundamental physical quantities, energy can be expressed in terms of force [F], acceleration [A], and time [T].
Given Fundamental Quantities:
- Force [F]
- Acceleration [A]
- Time [T]
Formula for Energy:
Energy (E) = Force (F) x Distance (D)
Dimensions of Energy:
- Energy = Force x Distance
- Distance = Acceleration x Time^2 (from the formula for acceleration)
- Therefore, Energy = Force x (Acceleration x Time^2)
- Substituting the fundamental quantities, Energy = [F][A][T^2]
Therefore, the correct dimensions of energy in terms of force [F], acceleration [A], and time [T] are [F][A][T^2], which corresponds to option 'B'.
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If force [F], acceleration [A] and time [T] are chosen as the fundame...
Energy, E ∝ Fa AbTc
[E] = [Fa][Ab][Tc]
⇒ [ML2T−2] = [MLT−2]a[LT−2]b[T]c
[ML2T−2] = [MaLa+bT−2a−2b+c]
Comparing dimensions on both sides.
⇒ a = 1 ; a + b = 2 and −2 = −2a − 2b + c
⇒ b = 1 ⇒ −2 = −2 −2 + c
⇒ c = 2
[E] = [F AT2]
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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]b)[F][A][T2]c)[F][A][T−1]d)[F][A−1][T]Correct answer is option 'B'. Can you explain this answer?
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