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

The $x$ and $y$ displacements of a particle are given as $x(t) = a \sin \omega t$ and $y(t) = a \sin 2 \omega t$. Its trajectory will look like:

$A$ string of length $L$ fixed at one end carries a body of mass $m$ at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes an angle $\theta$ with the vertical. The angular frequency of the body is $\omega$. The tension in the string is

One end of a string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the center) will be ($T$ represents the tension in the string).

When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature $r$,the thrust on the road at the lowest point on the bridge will be

$A$ ball of mass $m$ is attached to the free end of an inextensible string of length $\ell$. Let $T$ be the tension in the string. The ball is moving in a horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be