A thin rod of negligible mass and area of cross-section 4 x 10 -6 m 2 , suspended vertically from one end, has a length of 0.5 m at 100 °C. The rod is cooled to 0° C but prevented from contracting by attaching a mass at the lower end. The value of this mass is (Given, coefficient of linear expansion is 10 -5 °C - 1 , Young's modulus is Y = 10 11 N m -2 and g = 10 m s -2 )
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(40)
The change in length due to decrease in temperature,
... (i)
Negative sign implies that length is decreasing. Now let M be the mass attached to the lower end. Then,
change in length due to suspension of load is
... (ii)
(from equations (i) and (ii))
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