Question

2. When a load of 10 N is hanged from a wire, the
elongation produced is x mm. If the wire goes over a
pulley and two weights 10 N each are hung at the
two ends, the elongation of the wire will be in mm)​

Answer 1

Answer:

x mm

Explanation:

Let L be the original length of wire and cross section area A.

Y be the young's modulus of elasticity.

When a load of 10 N is hanged from wire, the elongation produced is x mm.

We know that young's modulus of elasticity,Y=$\frac{tensile\;stress}tensile\;strain}=\frac{F\cdot L}{A\cdot l}$

Where F=applied force

L=Original length

l=Change in length=Elongation

A=Cross section area

Substitute the values then we get

$Y=\frac{10\cdot L}{Ax}$

If the wire goes over a pulley and two weight 10 N each are hung at the two ends.

At equilibrium position , length of wire=$\frac{L}{2}$ on each side

Then, Y=$\frac{10\cdot l}{2A l}$

$\frac{10\cdot L}{A\cdot x}=\frac{10\cdot L}{2Al}$

$l=\frac{x}{2}$

Elongation on each side=$\frac{x}{2}$

Total elongation =$\frac{x}{2}+\frac{x}{2}=x$ mm