Question

a rubber string of length 20m get elongated by 106mm due to its own weight when it is suspended vertically. If density of rubber is 1.5×10³ kg/m³,then find its young modulus of elasticity. (g=10m/s²)​

Answer 1

Refer the attachment for your answer...

Answer 2

Area of rubber band × length of band = volume of band

Let volume of band be V.

Let area of band be A.

Let mass of band be m.

We know that,

F/A = Y e/l

where F is force on the body

A is area of the body

Y is young's modulus of elasticity.

e is elongation

l is length of body

Here,

F = mg

A = V/l

So,

mg/(V/l) = Y e/l

mgl/V = Y e/l

density = m/V

density of rubber band (d) = 1.5×10^3 kg/m^3

so,

dgl = Y e/l

1.5×10^3×10×20 = Y 106×10^-3/20

Y = 1.5 × 10^7 ×400/106

Y = 5.66×10^7 kg /ms^-2 (nearly).

I hope my calculation is not wrong.