A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from 0c to 100c. Another rod of a different metal b having the same length expands by 0.045 cm for the same change in temperature, a third rod of the same length is composed of two parts one of metal a and the other of metal b. Thus rod expand by 0.06 cm.For the same change in temperature. The portion made of metal a has the length : (a) 20 cm (b) 10 cm (c) 15 cm (d) 18 cm
Answers
Explanation:
Given A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from 0c to 100c. Another rod of a different metal b having the same length expands by 0.045 cm for the same change in temperature, a third rod of the same length is composed of two parts one of metal a and the other of metal b. Thus rod expand by 0.06 cm.For the same change in temperature. The portion made of metal a has the length
We know that α = Δ L / LΔT
So α A = Δ L a / L ΔT
= 0.075 / 20 x 100
= 3.75 x 10^-5 / deg Celsius
Now α B = ΔLb / L Δ T = 0.045 / 20 x 100
= 2.25 x 10^-5 / deg Celsius.
So change in length will be
ΔL c = Δ L’a + Δ L’b
0.06 = L’a α A ΔT + L’b α b Δ T
L’ a + L’ b = 20
L’b = 20 – L’ a
0.06 = (3.75 L ‘a + 2.25 L’b) x 10^-3
60 = 3.75 L’a + 2.25 (20 – L’a)
1.5 L’a = 15
So L’a = 15/1.5
Or L’a = 10 cm