Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 103 kg, The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y =2.0 × 1011 Pa , g =9.8 m / s 2 ]

Question

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 103 kg, The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y =2.0 × 1011 Pa , g =9.8 m / s 2 ] (A) 3.60 × 10-8 (B) 2.60 × 10-7 (C) 1.87 × 10-3 (D) 7.07 × 10-4

Tardigrade Admin · Accepted Answer

Force on each column =( mg /4) Strain=( mg /4 AY ) =(50 × 103 × 9.8/4 × π(1-0.25) × 2 × 1011) =2.6 × 10-7

$3.60 \times 1 0^{- 8}$

$2.60 \times 1 0^{- 7}$

$1.87 \times 1 0^{- 3}$

$7.07 \times 1 0^{- 4}$

Force on each column $= \frac{m g}{4}$
Strain $= \frac{m g}{4 A Y}$
$= \frac{50 \times 1 0 ^{3} \times 9.8}{4 \times π ( 1 - 0.25 ) \times 2 \times 1 0 ^{11}}$
$= 2.6 \times 1 0^{- 7}$

Q. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50×103kg, The inner and outer radii of each column are 50cm and 100cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y=2.0×1011Pa,g=9.8m/s2 ]

3.60×10−8

2.60×10−7

1.87×10−3

7.07×10−4

Force on each column =4mg​ Strain=4AYmg​ =4×π(1−0.25)×2×101150×103×9.8​ =2.6×10−7

$3.60 \times 1 0^{- 8}$

$2.60 \times 1 0^{- 7}$

$1.87 \times 1 0^{- 3}$

$7.07 \times 1 0^{- 4}$

Force on each column $= \frac{m g}{4}$
Strain $= \frac{m g}{4 A Y}$
$= \frac{50 \times 1 0 ^{3} \times 9.8}{4 \times π ( 1 - 0.25 ) \times 2 \times 1 0 ^{11}}$
$= 2.6 \times 1 0^{- 7}$