The dimensional formula for Young’s modulus is

Question

The dimensional formula for Young’s modulus is (A) ML-1T-2 (B) M0LT-2 (C) MLT-2 (D) ML2T-2

Tardigrade Admin · Accepted Answer

Youngâs modulus =( textStress/ textStrain) Strees =( textForce/ textArea)⇒ [σ]=([MLT-2]/[L2]) =[ML-1T-2] Strain =( textChinge in length/ textOriginal length) Hence strain is dimensionless Hence [Y]=[ML-1T-2]

Q. The dimensional formula for Young’s modulus is

$M L^{- 1} T^{- 2}$

$M^{0} L T^{- 2}$

$M L T^{- 2}$

$M L^{2} T^{- 2}$

Young’s modulus $= \frac{Stress}{Strain}$
Strees $= \frac{Force}{Area} \Rightarrow [σ] = \frac{[ M L T ^{- 2} ]}{[ L ^{2} ]}$
$= [M L^{- 1} T^{- 2}]$
Strain $= \frac{Chinge in length}{Original length}$
Hence strain is dimensionless
Hence $[Y] = [M L^{- 1} T^{- 2}]$

Q. The dimensional formula for Young’s modulus is

ML−1T−2

M0LT−2

MLT−2

ML2T−2

Young’s modulus =StrainStress​ Strees =AreaForce​⇒[σ]=[L2][MLT−2]​ =[ML−1T−2] Strain =Original lengthChinge in length​ Hence strain is dimensionless Hence [Y]=[ML−1T−2]

$M L^{- 1} T^{- 2}$

$M^{0} L T^{- 2}$

$M L T^{- 2}$

$M L^{2} T^{- 2}$

Young’s modulus $= \frac{Stress}{Strain}$
Strees $= \frac{Force}{Area} \Rightarrow [σ] = \frac{[ M L T ^{- 2} ]}{[ L ^{2} ]}$
$= [M L^{- 1} T^{- 2}]$
Strain $= \frac{Chinge in length}{Original length}$
Hence strain is dimensionless
Hence $[Y] = [M L^{- 1} T^{- 2}]$