$A$ vehicle is moving on a track with constant speed as shown in the figure. The apparent weight of the vehicle is:

$A$ particle rotates in a horizontal circle of radius $R$ in a conical funnel with constant speed $V$. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):

An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ kmh^{-1}$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ ms^{-2}$)

$A$ particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $\ell$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity-free space. Then the stretch in the spring is

$A$ train is moving towards north. At one place it turns towards north-east,here we observe that

$A$ cyclist riding a bicycle at a speed of $14\sqrt{3} \text{ m/s}$ takes a turn around a circular road of radius $20\sqrt{3} \text{ m}$ without skidding. Given $g = 9.8 \text{ m/s}^2$,what is his inclination to the vertical in degrees?