Four identical hollow cylindrical columns, support a big structure of mass M . The inner and outer radii of a column are R1 and R2 respectively. Assuming the load distribution to be uniform, the compressional strain of each column is (where Y is Young’s modulus of the column)

Question

Four identical hollow cylindrical columns, support a big structure of mass M . The inner and outer radii of a column are R1 and R2 respectively. Assuming the load distribution to be uniform, the compressional strain of each column is (where Y is Young’s modulus of the column) (A) (Mg/π(R22-R12)Y) (B) (Mg/4π(R22-R12)Y) (C) (Mg/π(R12-R22)Y) (D) (Mg/4π(R12-R22)Y)

Tardigrade Admin · Accepted Answer

Area of cross-section of each column, A =π(R22-R12) Since each column supports one-quarter of the load. ∴ F=(Mg/4) Compressional strain of each column =(F/AY) =(Mg/4π(R22-R12)Y)

Q. Four identical hollow cylindrical columns, support a big structure of mass $M$ . The inner and outer radii of a column are $R_{1}$ and $R_{2}$ respectively. Assuming the load distribution to be uniform, the compressional strain of each column is
(where $Y$ is Young’s modulus of the column)

$\frac{M g}{π ( R _{2}^{2} - R _{1}^{2} ) Y}$

$\frac{M g}{4 π ( R _{2}^{2} - R _{1}^{2} ) Y}$

$\frac{M g}{π ( R _{1}^{2} - R _{2}^{2} ) Y}$

$\frac{M g}{4 π ( R _{1}^{2} - R _{2}^{2} ) Y}$

Area of cross-section of each column,
$A$ $= π (R_{2}^{2} - R_{1}^{2})$
Since each column supports one-quarter of the load.
$∴$ $F = \frac{M g}{4}$
Compressional strain of each column $= \frac{F}{A Y}$ $= \frac{M g}{4 π ( R _{2}^{2} - R _{1}^{2} ) Y}$

Q. Four identical hollow cylindrical columns, support a big structure of mass M . The inner and outer radii of a column are R1​ and R2​ respectively. Assuming the load distribution to be uniform, the compressional strain of each column is (where Y is Young’s modulus of the column)

π(R22​−R12​)YMg​

4π(R22​−R12​)YMg​

π(R12​−R22​)YMg​

4π(R12​−R22​)YMg​