Question

Problem 64b

Answer 1

Given information

It is given that there is a maximum height of a uniform vertical column made of granite that can support itself without buckling, and it is independent of the cross-sectional area

Further the Density of granite is given as :  

 

Step-by-step explanation

Step 1.

Stress is defined as force per unit area within materials that arises from externally applied forces

Mathematically, 

   

For a vertical column to stand without buckling, 

stress experienced by the column at its base due to its weight must be less than the compressive strength of the material(Compressive strength  is the capacity of a material to withstand loads tending to reduce size)

    

When :

  , the vertical column is on the verge of buckling and from this  condition we get the maximum height of the vertical column that can support itself without buckling