A vertical metal cylinder of radius 2 cm and length 2m is fixed at the

1.	A vertical metal cylinder of radius 2 cm and length 2m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young's modulus of the metal = 2 x 1011 N/m2.
Answer» (a) Length of the cylinder L = 2 m Area of cross-section A =πr² =π(2/100)² m² =4π/10000 m² Force on the cylinder F = 10010 N =1000 N Hence the stress =F/A =1000/(4π/10000) N/m² =(1/4π)10⁷ N/m² =0.0796 x10⁷ N/m² =7.96 x10⁵ N/m² (b) Strain = Stress/Y =(F/A)/Y ={7.96 x10⁵}/2.0 x10¹¹ =3.98 x10⁻⁶ ≈4 x10⁻⁶ (c) Let the compression of the cylinder = l m The strain =l/L = l/2 →4 x10⁻⁶ =l/2 →l =8 x10⁻⁶ m ρ= stress = mg/A e = strain = ρ/Y Compression ΔL = eL

A vertical metal cylinder of radius 2 cm and length 2m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young's modulus of the metal = 2 x 1011 N/m2.

Answer»

(a) Length of the cylinder L = 2 m

Area of cross-section A =πr² =π(2/100)² m² =4π/10000 m²

Force on the cylinder F = 100*10 N =1000 N

Hence the stress =F/A =1000/(4π/10000) N/m²

=(1/4π)*10⁷ N/m²

=0.0796 x10⁷ N/m²

=7.96 x10⁵ N/m²

(b) Strain = Stress/Y =(F/A)/Y

={7.96 x10⁵}/2.0 x10¹¹

=3.98 x10⁻⁶ ≈4 x10⁻⁶

The strain =l/L = l/2

→4 x10⁻⁶ =l/2

→l =8 x10⁻⁶ m

ρ= stress = mg/A

e = strain = ρ/Y
Compression ΔL = eL