Question

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 1

 (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  

(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

Answer 2

ρ= stress = mg/A

e = strain = ρ/Y
Compression ΔL = eL