A wire elongates by 9mm when a load of 10kg is suspended from it. What is the elongation when it's radius is doubled, if all the other quantitites are as same as before?
Ans= 2.25 mm
HELP PLEASE! :O
we know that teh Young's modulus is given as
Y = F.L0 / A0.ΔL
so, elongation will be
ΔL = F.L0 / A0.Y
now, in the first case
A0 = πr02
F = mg = 9kg x 9.8m/s2 = 88.2 N
ΔL = 9mm = 0.009m
now, in the second case
as the radius is doubled
A'0 = π(2r0)2 = 4A0
and other quantities remains same
so,
elongation will be
ΔL' = F.L0 / A'0.Y
= F.L0 / 4A0.Y
or
ΔL' = ΔL / 4
= 9mm / 4
thus,
ΔL' = 2.25 mm
Y = F.L0 / A0.ΔL
so, elongation will be
ΔL = F.L0 / A0.Y
now, in the first case
A0 = πr02
F = mg = 9kg x 9.8m/s2 = 88.2 N
ΔL = 9mm = 0.009m
now, in the second case
as the radius is doubled
A'0 = π(2r0)2 = 4A0
and other quantities remains same
so,
elongation will be
ΔL' = F.L0 / A'0.Y
= F.L0 / 4A0.Y
or
ΔL' = ΔL / 4
= 9mm / 4
thus,
ΔL' = 2.25 mm