MHT CET · Physics · Thermal Properties of Matter
Two black spheres P & Q have radii in the ratio \(4: 3\). The wavelength of maximum intensity of radiation are in the ratio \(4: 5\) respectively. The ratio of radiated power by P to Q is
- A \(\frac{625}{144}\)
- B \(\frac{125}{81}\)
- C \(\frac{25}{9}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{625}{144}\)
Step-by-step Solution
Detailed explanation
\( \frac{T_P}{T_Q} = \frac{\lambda_{max,Q}}{\lambda_{max,P}} = \frac{5}{4} \) \( \frac{P_P}{P_Q} = \left(\frac{R_P}{R_Q}\right)^2 \left(\frac{T_P}{T_Q}\right)^4 = \left(\frac{4}{3}\right)^2 \left(\frac{5}{4}\right)^4 = \frac{16}{9} \times \frac{625}{256} = \frac{625}{144} \)
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