A particle is projected from ground at an angle $\mathrm{\theta }$. At a certain instant the velocity vector $\overrightarrow{v}$ of particle makes an angle $\mathrm{\alpha }$ with horizontal. Choose the correct option(s).

 A particle $P$ of mass $m$ is attached to a vertical axis by two strings $AP$ and $BP$ of length $l$ each. The separation $AB=l$. $P$ rotates around the axis with an angular velocity $\omega$. The tensions in the two strings are $T_1$ and $T_2$. Choose the correct option(s).

On a train moving along east with a constant speed $v$, a boy revolves a bob with string of length $l$ on smooth surface of train, with equal constant speed $v$ relative to train. Mark the correct option(s).

Consider the figure shown below. A block $B$ is kept on a rotating rough table over which a man stands. Another man $A$ stands on the ground. Choose the correct option(s).

One end of a light inextensible string of length $l$ is attached to a particle of mass $m$ resting on a smooth horizontal table. The string passes through a smooth hole in the table and its other end is attached to a small particle of same mass. The system is set in rotation as shown in figure with constant angular speed. Choose the correct option(s).

A bob of mass $m$ hangs by a light inextensible string which is connected with a rigid support after passing over a smooth pulley $P$. If the bob is released from an angular position $\mathrm{\theta }=30°$, then

A force of constant of magnitude $F$ acts on a particle (mass $m$) moving in a plane such that it is always perpendicular to the velocity $\overrightarrow{v}\left(\left|\overrightarrow{v}\right|=v\right)$ of the body. Select the correct option(s).