If speed V , force F and acceleration a are chosen as the fundamental physical quantities, then the dimension of Young's modulus in terms of V , F and a are

Question

If speed V , force F and acceleration a are chosen as the fundamental physical quantities, then the dimension of Young's modulus in terms of V , F and a are, V - 3 Fa, V - 4 F 2 a 2, V - 4 Fa 2, V - 4 F 2 a

MARKS App · Accepted Answer

Let Y = f V , F , a ∴ Y = KV x F y a z , K → Unitless ∴ Y = V x F y a z ∴ ML - 1 T - 2 = LT - 1 x MLT - 2 y LT - 2 z ∴ M L - 1 = T - 2 = M y L x + y + z T - x - 2 y - 2 z ∴ y = 1 ; x + y + z = - 1 ; - x - 2 y - 2 z = 2 ∴ x + z = - 2 ∴ x + 2 y + 2 z = 2 ∴ x + 2 z = 0 ∴ z = 2 , x = - 4 ∴ Y = V - 4 Fa 2

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