A block of mass $M$ lies at rest connected to a massless spring of spring constant $k$ on a frictionless surface. A bullet of mass $m$ hits the block horizontally with speed $v$ as shown in the figure and is completely stuck to the block. What is the maximum compression in the spring resulting from this impact (assuming that at this point the spring is still not fully compressed)?

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?