A particle moves in a circle uniformly such that it completes a circle in $2 \mathrm{s}$. During half a turn its centripetal acceleration change by $6 \mathrm{m} {\mathrm{s}}^{-2}$. 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).

A bead of mass $m$ can slide without friction on a fixed vertical loop of radius $R$. The bead moves under the combined effect of gravity and a spring with spring constant $k$ only. The spring is rigidly attached to the bottom of the loop. Assume that the natural length of spring is zero. The bead is released from rest at $\mathrm{\theta }=0°$ with non-zero but negligible speed to the bead. The gravitational acceleration is directed downward as shown in the figure. Now choose the correct option(s). (Neglect any type of friction between any contact) (given $kR=mg/2$)