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प्रश्न
If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula ______.
पर्याय
(P1 A–1 T1)
(P2 A1 T1)
(P1 A–1/2 T1)
(P1 A1/2 T–1)
उत्तर
If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula `underline((P^1 A^(1/2) T^(-1))`.
Explanation:
Let us consider in terms of fundamental quantities, the dimensional formula of energy be P, A and T be [PaAb Tc]. Where P is the momentum, whose dimensional formula is [MLR–1], A is the area whose dimensional formula is [L2] and T is a time whose dimensional formula is [T1]
∴ Energy = F.s
= [MLR–2] [L]
= [ML2T–2]
∴ [ML2T–2] = [MLT–1]a[L2]b[T]c
[M1L2T–2] = [MaLa+2bTa+c]
Comparing the powers we get,
a = 1
1 + b = 2
2b = 2 – 1
b = `1/2`
– a + c = – 2
– 1 + c = – 2
c = – 2 + 1
c = – 1
∴ The dimensional formula of energy is `[P^1 A^(1/2) T^-1].`
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