Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is p q (where p and q are least positive integers)

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Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is p q (where p and q are least positive integers). The value of p + q is

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Correct answer: 2

Energy radiated E = σ T 4 × 4 π R 2 × time × e E 1 E 2 = 4000 4 × 1 2 × 1 × 4 π σ e 2000 4 × 4 2 × 1 × 4 π σ e = 1 1 .

Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is p q (where p and q are least positive integers). The value of p + q is

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