Question

A steel wire is suspended vertically from a rigid support when loaded with a weight in air it expands by l a and when it is immersed completely inverter the extension is reduced lw than relative density of the material will be

Answer 1

The Young's Modulus of a material is given as

Y = FL0 / A0.dL

here F is the net force

L0 is the original length (same in both cases)

A0 is the original area of cross-section (same in both cases)

dL is the change in length

now, when the wire is in air we have

Y = FL0 / A0.La (1)

here F = mg (weight of the wire)

and when the wire is in water

Y = F'L0 / A0.Lw

now, here F' = weight of the wire - upthrust of water = mg - ρgV

here V is the volume of the wire and ρ is the density of water

so,

Y = [(mg - ρgV)L0 ]/ A0.Lw (2)

now as equation (1) and (2) are equal, we have

FL0 / A0.La = [(mg - ρgV)L0 ]/ A0.Lw

or

mg / La = [(mg - ρgV) / Lw

ρV / m = 1 - (Lw / La)

now as m/V= ρ' which is the density of the wire, we have

ρ / ρ' = 1 - (Lw / La) = (La - Lw) / La

or

the relative density will be

ρ' / ρ = La / (La - Lw)

Answer 2

hey , hope this helps !!!!!!!!!!!!!