Young’s modulus for a steel wire is 2 × 1011 Pa and its elastic limit is 2.5 × 108 Pa. By how much can a steel wire 3 m long and 2 mm in diameter be stretched before the elastic limit is exceeded?

Question

Young’s modulus for a steel wire is 2 × 1011 Pa and its elastic limit is 2.5 × 108 Pa. By how much can a steel wire 3 m long and 2 mm in diameter be stretched before the elastic limit is exceeded? (A) 3.75 mm (B) 7.50 mm (C) 4.75 mm (D) 4.00 mm

Tardigrade Admin · Accepted Answer

The cross-sectional area of a wire of radius

r = 1 mm = 1 0^{- 3} m

is

A = π r^{2} = 3.14 \times 1 0^{- 6} m^{2}

The maximum force that can be applied without exceeding the elastic limit is therefore

F = (\frac{F}{A})_{m a x} \times (A)

= (2.5 \times 1 0^{8} N m^{- 2}) (3.14 \times 10 - 6 m^{2}) = 785 N

When this force is applied, the wire will stretch by

Δ L = \frac{L}{Y} \frac{F}{A} = \frac{( 3 m ) ( 785 N )}{( 2 \times 1 0 ^{11} N / m ^{2} ) ( 3.14 \times 1 0 ^{- 6} m ^{2} )}

= 3.75 \times 1 0^{- 3} m = 3.75 mm

Q. Young’s modulus for a steel wire is 2×1011Pa and its elastic limit is 2.5×108Pa. By how much can a steel wire 3 m long and 2mm in diameter be stretched before the elastic limit is exceeded?

3.75 mm

7.50 mm

4.75 mm

4.00 mm

Q. Young’s modulus for a steel wire is $2 \times 1 0^{11} P a$ and its elastic limit is $2.5 \times 1 0^{8} P a$ . By how much can a steel wire 3 m long and $2 mm$ in diameter be stretched before the elastic limit is exceeded?