Question

A solid cylindrical steel column is 4 m long and 9 cm in diameter . (Ysteel = 1.9 × 1011 Nm–2). The decrease in length of the column, while carrying a load of 80000 kg is.........

(A) 3.2 mm

(B) 1.8 mm

(C) 4.4 mm

(D) 2.6 mm

Answer 1

The correct option is (D) 2.6 mm.

Explanation:

Y = (FL / Aℓ) (1)

L = 4m

A = {(πd2) / 4} = (π/4) × (9 × 10–2)2

∴ A = 63.61 × 10–4 m2

Y = 1.9 × 1011 N/m2

F = mg = 80000 × 10 = 8 × 105 N

Now from (1)

ℓ = (FL / YA)

∴ ℓ = {(8 × 105 × 4) / (1.9 × 1011 × 63.61 × 10–4)}

= 0.26 × 10–2 m

= 2.6 × 10–3 m ℓ

= 2.6 mm