JEE Main 2014 · 6 Apr · Shift 1 · Physics Q11

← JEE Main 2014 · 6 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 11 of 90

Three rods of Copper, Brass and Steel are welded together to form a Y - shaped structure. Area of cross - section of each rod $=4$ cm $^2$ . End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

1.2 cal/s

2.4 cal/s

4.8 cal/s

6.0 cal/s

Answer and worked solution

Official answer: C

Let the junction be at $\theta$ . Heat into the junction through copper equals heat out through brass and steel (with $A$ common):
$\frac{0.92(100-\theta)}{46}=\frac{0.26\,\theta}{13}+\frac{0.12\,\theta}{12}\implies0.02(100-\theta)=0.03\,\theta\implies\theta=40^\circ\text{C}.$
Rate through copper:
$\frac{0.92\times4\times60}{46}=4.8\text{ cal/s}.$

Topics:Conduction

← Previous question Next question →

JEE Main 2014 · 6 Apr · Shift 1, Physics question 11