Question

19. A rod 3 m long is heated from 10°C to 90°C. Find the expansion of rod. Take Young’s modulus = 1.0 x 10^5 MN/m2 and coefficient of thermal expansion = 0.000012 per degree centigrade.

Answer 1

Given : A rod 3 m long is heated from 10°C to 90°C. Take Young’s modulus = 1.0 x 10^5 MN/m2 and coefficient of thermal expansion = 0.000012 per degree centigrade.

To Find :    expansion of rod.

Solution:

ΔL  = L α ΔT

L = 3m

ΔT = 90°C - 10°C = 80°C

α = 0.000012 per degree centigrade = 12 x 10⁻⁶ /°C

ΔL = 3 *  12 x 10⁻⁶ * 80

=> ΔL =2880 x 10⁻⁶

=>  ΔL = 0.288  x 10⁻²  m

=>  ΔL = 0.288  cm

=> ΔL = 2.88 mm

expansion of rod.  = 2.88 mm

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Answer 2

${ \red{ \bf{ Given: }}}$

Length of rod = 3m

Heated from 10°C to 90°C

Let's take Young's modulus = 1.0 x 10^5 MN/m2

Let's take coefficient of thermal expansion = 0.000012 per degree centigrade.

${ \red{ \bf{ To \: Find: }}}$

Expansion of rod

${ \red{ \bf{ Solution: }}}$

AL = La AT

L = 3m

AT90°C 10°C = 80°C

a = 0.000012 per degree centigrade = 12 x 10-6/°C

AL=3 × 12 x 10-6 × 80

AL =2880 x 10-6

AL = 0.288 x 10-² m

AL = 0.288 cm

AL = 2.88 mm

${ \red{ \bf{ Therefore, \: expansion \: of \: rod = 2.88 mm}}}$