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GATE 2025 ME – Question 33

Casting, Forming and Joining Processes · Welding, brazing, soldering and adhesive bonding · 1 mark · Numerical answer

During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, 85% is absorbed within a circle of radius 5 mm while 65% is absorbed within an inner concentric circle of radius 3 mm. The power density in the shaded area is __________ W mm$^{-2}$ (rounded off to 2 decimal places).

Two concentric circles, an inner one of radius 3 mm and an outer one of radius 5 mm. The ring between them is shaded.

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Correct answer: 9.90 to 10.00

Explanation

The power absorbed in the shaded ring is $(0.85 - 0.65) \times 2500 = 500$ W. The area of the ring is $\pi(5^2 - 3^2) = 16\pi = 50.27$ mm$^2$. The power density is $\frac{500}{50.27} = 9.95$ W/mm$^2$.