Two cars $A$ and $B$ start racing at the same time on a flat race track which consists of two straight sections each of length $100\mathrm{\pi }$ and one circular section as shown in the figure. The rule of the race is that each car must travel at constant speed at all times without even skidding.

Consider the setup of a Ferris wheel in an amusement park. The wheel is turning in a counterclockwise manner. Contrary to the illustration, not all seats are aligned horizontally, i.e., parallel to the: $x$-axis. Determine the orientation of the normal to seat as it passes point $A$.

A particle of mass $m$ moves along a circular path of the radius $r$ with a centripetal acceleration $a_n$ changing with time $t$ as $a_n=k{t}^2$, where $k$ is a positive constant. The average power developed by all the forces acting on the particle during the first $t_0$ seconds is: 
(Given that initial speed $u=0$.)

A collar $B$ of mass $2 \mathrm{kg}$ is constrained to move along a horizontal smooth and fixed circular track of radius $5 \mathrm{m}$. The spring lying in the plane of the circular track and having spring constant $200 \mathrm{N} {\mathrm{m}}^{-1}$ is undeformed when the collar is at $A$. If the collar starts from rest at $B$, the normal reaction exerted by the track on the collar when it passes through $A$ is

A mass $m$ starting from $A$ reaches $B$ of a frictionless track. On reaching $B$, it pushes the track with a force equal to $x$ times its weight, then the applicable relation is

Figure shows a smooth vertical circular track $AB$ of radius $R$. A block slides along the surface $AB$ when it is given a velocity equal to $\sqrt{6gR}$ at point $A$. The ratio of the force exerted by the track on the block at point $A$ to that at point $B$ is:

A bead of mass $m$ is released from rest at $A$ to move along the fixed smooth circular track as shown in the figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point $P_0$ described by the angle $\theta \left(\ne 0\right)$ would