Four identical hollow cylindrical cloumns of steel support a big structure of mass 50.000 kg. the inner and outer radii of each column are 30 cm and 60 cm respectively. Assume the load distribution to be uniform , calculate the compressional strain of each column. the Young's modulus of steel is `2.0 xx 10^(11) Pa`.

Options

A. `(Mg)/(pi(R_(2)^(2)- R_(1)^(2))Y)`
B. `(Mg)/(4pi(R_(2)^(2)- R_(1)^(2))Y)`
C. `(Mg)/(pi(R_(1)^(2)- R_(2)^(2))Y)`
D. `(Mg)/(4pi(R_(1)^(2)- R_(2)^(2))Y)`

Answer

B

Explanation

Area of cross-section of each column, `A= pi(R_(2)^(2) - R_(1)^(2))`
Since each column supports one-quarter of the load `therefore" " F= (Mg)/(4)`
Compressinal strain of eacch column `= (F)/(AY) = (Mg)/(4pi(R_(2)^(2) - R_(1)^(2))Y)`