A plastic dowel has a Young's Modulus of 1.50 ✕ 1010 N/m2. Assume the dowel will break if more than 1.50 ✕ 108 N/m2 is exerted. (a) What is the maximum force (in kN) that can be applied to the dowel assuming a diameter of 2.40 cm?
Kn
(b) If a force of this magnitude is applied compressively, by how much (in mm) does the 26.0 cm long dowel shorten? (Enter the magnitude.)
mm

a

b

Explanation:

From the question we are told that

      The Young modulus is  

      The stress is  

      The  diameter is  

The radius is mathematically represented as

The cross-sectional area is  mathematically evaluated as

Generally the stress is mathematically represented as

=>    

=>    

=>    

Considering part b

      The length is given as

Generally Young modulus is mathematically represented as

Here strain is mathematically represented as

So    

=>    

substituting values

Converting to mm

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .