A wire, 3 m in length and 1 mm in diameter at 30° C is kept in low temperature at -170° C and is stretched by hanging a weight of 10 kg at one end. The change in length of the wire is [.Y=2× 1011 N m- 2 , g=10 ms- 2 and α =1.2× 10- 5/° C].

Question

A wire, 3 m in length and 1 mm in diameter at 30° C is kept in low temperature at -170° C and is stretched by hanging a weight of 10 kg at one end. The change in length of the wire is [.Y=2× 1011 N m- 2 , g=10 ms- 2 and α =1.2× 10- 5/° C]. (A) 5.2mm (B) 2.5mm (C) 7.2mm (D) 3.5mm

Tardigrade Admin · Accepted Answer

The change in length of the wire due to change in temperature

= αL T = 1.2 \times (10)^{- 5} \times 3 \times (- 170 - 30)

= - 7.2 \times 1 0^{- 3} m

The change in the length of the wire due to the stretching force

= \frac{F L}{A Y} = \frac{10 \times 10 \times 3}{0.75 \times 1 0 ^{- 6} \times 2 \times 1 0 ^{11}}

= 2 \times 1 0^{- 3} m

The total change in the length of the wire

= - 7.2 \times 1 0^{- 3} + 2 \times 1 0^{- 3}

= - 5.2 \times 1 0^{- 3} m = - 5.2 mm

The negative sign indicates contraction of the wire

$5.2 mm$

$2.5 mm$

$7.2 mm$

$3.5 mm$

Q. A wire, 3m in length and 1mm in diameter at 30∘C is kept in low temperature at −170∘C and is stretched by hanging a weight of 10kg at one end. The change in length of the wire is [Y=2×1011 Nm−2 , g=10ms−2 and α=1.2×10−5/∘C]

5.2mm

2.5mm

7.2mm

3.5mm

$5.2 mm$

$2.5 mm$

$7.2 mm$

$3.5 mm$