Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times {10}^{3}kg .$ 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 $Y = 2 . 0 \times {10}^{11}Pa, g = 9 . 8m{s}^{- 2}$ ]

Question

Four identical hollow cylindrical columns of mild steel support a big structure of mass

50 \times {10}^{3}kg .

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 \times {10}^{11}Pa, g = 9 . 8m{s}^{- 2}

]

Quantrex Academy · Accepted Answer

Correct answer: B. 2 . 60 × 10 ^ - 7

( )/(L) = (mg)/(4AY) = 50 × 10 ^ 3 × 9 . 8 4π( 100 ^ 2 - 50 ^ 2 ) × 10 ^ - 4 × 2 × 10 ^ 11 = 5 × 10 ^ 5 4 × π × 150 × 50 × 10 ^ - 4 × 2 × 10 ^ 11 (Δ L)/(L) = (1)/(12π) × 10 ^ - 5 = 2 . 60 × 10 ^ - 7

Four identical hollow cylindrical columns of mild steel support a...

Options

Correct answer

Step-by-step solution

More from Mechanical Properties of Solids