A metallic cube initially kept at a temperature $T$ is emitting black body radiation with a power $P$ (energy emitted per unit time). If $T$ is increased by $1 \%$, the power being radiated increases by $4.5 \%$. What is the approximate percentage increase in the volume of the cube in this process?

Consider two pipes $A$ and $B$ of identical length. $A$ has one end closed and one end open. $B$ has both ends open. Each tube is immersed in a closed chamber of ideal gas having volume $V$. The chamber containing tube $A$ is at temperature $T_A$ and the chamber containing tube $B$ is at temperature $T_B$. The sound frequencies corresponding to the $n_A$-th harmonic in tube $A$ and the $n_B$-th harmonic in tube $B$ are the same. What is the relation between the temperatures $T_A$ and $T_B$ ?

Consider two waves, which are given by $y_1(x, t)=A \sin (k x-\omega t)$ and $y_2(x, t)=\sqrt{3} A \cos (k x-\omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. The amplitude of the resultant waveform obtained by the superposition of the two waves is $A_s$ and its phase difference with $y_1$ is $\phi_s$. What are $A_s$ and $\phi_s$ ?

A particle of charge $q=1 e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates of length $l$ as illustrated in the figure. The potential difference between the two plates is 1 V and their separation is $d$. What is the minimum value of $K$ (in eV ) for which the particle will not hit either of the plates? [ $e$ is the charge of the electron.]