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:

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).

$A$ cyclist goes round a circular path of circumference $34.3 \ m$ in $\sqrt{22} \ s$. The angle made by him with the vertical will be ....... $^o$.

$A$ rod $(AB)$ is attached to a fixed point $(C)$ using a light rope $(AC)$. The other end of the rod $(B)$ is resting on ice with negligible friction,and the system is in a stationary position. Which of the following can be the equilibrium configuration of this system?

In a conical pendulum,the bob of mass $m$ moves in a horizontal circle of radius $r$ with uniform speed $V$. The string of length $L$ describes a cone of semi-vertical angle $\theta$. The centripetal force acting on the bob is $(g = \text{acceleration due to gravity})$

$A$ string of length '$L$' fixed at one end carries a mass '$m$' at the other end. The string makes $\frac{3}{\pi}$ r.p.s. around the vertical axis through the fixed end. The tension in the string is (in $mL$)