Dimensional formula for young‘s modulus of elasticity is
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Young's modulus is the ratio of stress (which has units of pressure) to strain (which is dimensionless), and so Young's modulus has units of pressure. Its SI unit is therefore the pascal (Pa or N/m2 or kg. m. s−2).
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Young's modulus = Stress/Strain
= F/A x e/l
= ma/A x e/l
Where,
F = force
A = area of cross section
e = elongation
l = actual length
a = acceleration
m = mass
By their units,
Y = [(kg x m/s²) / (m²)] x m/m
Y = (Kg x m) / (m²s²)
Y = Kg/ms²
In dimension formula Y = [ M L⁻¹ S⁻²]
= F/A x e/l
= ma/A x e/l
Where,
F = force
A = area of cross section
e = elongation
l = actual length
a = acceleration
m = mass
By their units,
Y = [(kg x m/s²) / (m²)] x m/m
Y = (Kg x m) / (m²s²)
Y = Kg/ms²
In dimension formula Y = [ M L⁻¹ S⁻²]
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