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If instead of mass, length and time as fundamental quantities, we choose velocity, acceleration and force as fundamental quantities and express their dimensions by v , a and F respectively, then the dimensions of Young's modulus will be expressed as

If instead of mass, length and time as fundamental quantities, we choose velocity, acceleration and force as fundamental quantities and express their dimensions by vand respectively, then the dimensions of Young's modulus will be expressed as

Grade:11

1 Answers

Arun
25763 Points
3 years ago

Young’s Modulus is given by,

Y = Stress/Strain

Stress = Force/Area

Strain = change in length/length = dimensionless

Therefore, dimension of Y is [ML-1T-2]

Let,

[FxAyVz]  = [ML-1T-2]

=> [MLT-2][LT-2]y [LT-1]z = [ML-1T-2]

=> [Mx Lx+y+z T-2x-2y-z] = [ML-1T-2]

Thus,

x = 1

x+y+z = -1

-2x-2y-z = -2

Solving we get,

x = 1, y = 2, z = -4

So, the required dimension is [FA2V-4]

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