Question

A mass of 5kg is suspended from vertical wite of 1m length and radius 1mm . If the youngs modulus of the material of the wire be 2 x 10 ¹² dyne/cm2. Find the length of the wire without load.​

Answer 1

Solution :-

As per the given data ,

• Mass(m) = 5 kg =  5000 g
• Length of the wire(L) = 1 m = 100 cm
• Young's modulus (γ) =   2 x 10 ¹² dyne / cm²

• Radius of the wire (r) = 1 mm  = 0.1 cm

Young's modulus is given by the formula ,

➸ γ = F / A  /  Δ L / L

➸ γ = F x L / A x ΔL ... (1)

Here ,

By applying Newton's second law of motion ,

➸ F = mg

➸ F = 5000  g x 980 cm / s²

➸ F = 49,00,000 g cm / s²

➸ F = 49 x 10 ^5 N

We know that ,

➸ A = π r ²

➸ A = 3.14 x 0.01

➸ A = 0.0314 cm²

Now let's substitute the values of F and A  in eq 1  ,

➸ 2 x 10 ¹² =49 x 10 ^5 x 100 / 0.0314 x ΔL

➸ ΔL = 49 x 10 ^5 x 100 / 0.0314 x 2 x 10 ¹²

➸ ΔL = 49 x 10 ^7 / 628 x 10 ^8

➸ ΔL = 0.078 x 10^-1

➸ ΔL = 0.0078 cm

The length of the wire without load is 0.0078 cm