$A$ mass $m$ is attached to one end of a spring with spring constant $k$ and natural length $l$. The system is rotated in a horizontal plane with an angular velocity $\omega$. What is the extension in the length of the spring?

$A$ stone of mass $2 \,kg$ is tied at one end of a string of length $2 \,m$ and is whirled in a horizontal circle. If the string can withstand a maximum tension of $64 \,N$, then the permissible maximum number of rotations per minute is

Two particles of mass $2m$ and $m$ are attached to a light string as shown. The complete system is rotated in a horizontal circle with a constant angular velocity $2\omega$ about an axis passing through point $O$ and perpendicular to the plane of the circle. Find the ratio $T_{OA} / T_{AB}$,where $T_{OA}$ and $T_{AB}$ are the tensions in strings $OA$ and $AB$ respectively.

$A$ particle starts from rest and performs circular motion of constant radius with speed given by $v = \alpha \sqrt{x}$,where $\alpha$ is a constant and $x$ is the distance covered. The correct graph of the magnitude of its tangential acceleration $(a_t)$ and centripetal acceleration $(a_c)$ versus $t$ will be:

If a stone of mass $0.5 \ kg$ tied to one end of a wire is whirled in a circular path of radius $2 \ m$ with a speed $40 \ rev/min$ in a horizontal plane,then the tension in the wire is nearly (in $N$)

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. Then the force exerted by the liquid at the other end is