Question

A wire of length L1 and area of cross section A is attached to a rigid support . Another metal wire of length L2 and of the same cross sectional area is attached to a free end of the first wire .Am boy of mass M is suspended from the free end of the second wire .If Y1 ans Y2 are the young moduli of the wire respectively the effective force constant of the system of two wire is

Answer 1

we know, Young's modulus = stress/strain

strain = original length/change in length

Let original length of wire = L at 0°C

after 100°C, due to thermal expansion length of wire increases .

so, length or wire at 100°C , L' =L(1 + α∆T)

here, α is linear coefficient of expansion and ∆T is the change in temperature.

so, L' =L + Lα(100- 0) = L + 100αL

L' - L = ∆L = 100αL

hence, change in length , ∆L = 100αL

now, Young's modulus = stress/strain

Y = stress/{∆L/L}

stress = {∆L/L} × Y = (100αL/L) × Y

stress = 100αY

hence, stress = 100αY