A cart of mass $M$ is released from $A$, the highest point of a frictionless track, as shown in the figure. The cart travels along the track and enters the semicircular arc $D B C$ of radius $R$. The heights of the points $A$ and $B$ are $h_1$ and $h_2$ from the ground, respectively. Which of the following quantities does not play any role in ensuring that the cart does not leave the track?

A circular disk of mass $M$ and radius $R$ is rotating clockwise with a uniform angular velocity $\omega$ about an axis passing through the centre, normal to the disk. At time $t=0$, a torque $T$ is applied along the same axis to oppose the rotation of the disk. What is the angular displacement $\theta$ (measured from $t=0$ in the clockwise direction) that the disk attains before it starts rotating counterclockwise?

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 $T_B$ ?