Question

A circular **** in an aluminium plate is 2.54 cm in diameter at 0°C. What is the diameter when the temperature of the plate is raised to 100°C ? Given α Al = 2.3 × 10–5 (°C)–1

(1) 2.54

(2) 1.25

(3) 3.55

(4) 4.25

Answer 1

Correct Answer is: (1) 2.54

Let Do and Dt be diameters of **** at 0°C and t°C respectively.

Circumference of **** at 0°C

l = 2πr0 = πD0

Circumference of **** at t = 100° C

lt = 2πlt = πDt

From relation lt = l0 (1 + α.t), we get

πDt = πD0(1 + 2.3 × 10–5 × 100)

Dt = 2.54 ( 1 + 0.0023)

= 2.5458 cm.