A rubber string 10 m long is suspended from a rigid support at its one end. Calculate the extension in the string due to its own weight. The density of rubber is 1.5*10^3 kg m^-3 and yong modulus for the rubber is 5*10^6Nm^-2. Take g=10
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we know that Young's modulus is given as
Y = FL0/A0ΔL
or
the extension in string will be
ΔL = FL0/A0Y
here,
F = weight of sting = mg = density x volume x g = ρ x πr2L0 x g
where, ρ = 1.5*103 Kg m-3, r = radius of cross-section and L0 = 10m
we would also require the value of area of cross-section A0 or radius r
and
Y = 5*106 N/m2
using the above values and A0 we can find ΔL
Y = FL0/A0ΔL
or
the extension in string will be
ΔL = FL0/A0Y
here,
F = weight of sting = mg = density x volume x g = ρ x πr2L0 x g
where, ρ = 1.5*103 Kg m-3, r = radius of cross-section and L0 = 10m
we would also require the value of area of cross-section A0 or radius r
and
Y = 5*106 N/m2
using the above values and A0 we can find ΔL
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