Thermal Properties of Mat question bank (Physics)

Two spherical stars, A and B emit black body radiation. The radius of star A is $400$ times that of star B and star A emits power $10^4$ times emitted from star B. $\lambda_A$ and $\lambda_B$ are the wavelengths at which the peak occurs in their respective radiation curves such that $\lambda_A = x\,\lambda_B$. The value of $x$ is

A clock with an iron pendulum keeps the correct time at $14^\circ\text{C}$. If the room temperature is $20^\circ\text{C}$, the error in a second per day will be nearly (coefficient of linear expansion of iron is $1.2 \times 10^{-5} / {}^\circ\text{C}$ )