Question

The modulus of elasticity is dimensionally equivalent to

a.strain

b.stress

c.surface tension

d.poisson's ratio

Answer 1

The modulus of elasticity is dimensionally equivalent to Stress.

Answer 2

Answer: The dimension formula of modulus of elasticity is equivalent to stress.

Explanation:

We know that,

The modulus of elasticity is the ratio of the stress and strain.

$Y = \dfrac{stress}{strain}$

Strain is unit less.

Therefore,

The dimension formula of modulus of elasticity is

$Y = \dfrac{ML^{-1}T^{-2}}{unitless}$

$Y = {ML^{-1}T^{-2}$......(I)

We know that,

The stress is the force upon area.

Stress = $\dfrac{F}{A}$

The dimension formula of stress

Stress = $ML^{-1}T^{-2}$....(I)

From eqyation (I) and (II)

$Y = {ML^{-1}T^{-2}$= stress

Hence, The dimension formula of modulus of elasticity is equivalent to stress.