Question

8. A rod of length 20 cm is made of metal. It expands by
0.075 cm when its temperature is raised from 0°C to
100°C. 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​

Answer 1

Answer:

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

Explanation: