Question

A thin uniform elastic rod of natural length l,density and young's modulus y is just completely immersed in vertical position in fluid of density 2 by applying a vertical downward force at its top end. The rod is in equilibrium,then find the magnitude of net compression in rod.

Answer 1

The magnitude of net compression in the coil is 2FL / AY.

Explanation:

Y = T / A . ds/dx

=> T / AY . dx

=>T = (3F - 2F / Lx)

∫ ds = ∫ L - 0 F / AY ( 3 - 2 /Lx) dx

∫ ds =  F / AY (3x - x^2 / L) | L - 0

Magnitude of net compression =  F / AY ( 3L - L ) = 2fL / AY

Thus the magnitude of net compression in the coil is 2FL / AY.

Answer 2

Answer:take T=Apg(2L-x)

Explanation: