$A$ body of mass $5\, kg$ is moving in a circle of radius $1\, m$ with an angular velocity of $2\, rad/s$. The centripetal force is ......... $N$.

$A$ 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?

$A$ small $100 \ g$ sleeve $B$ can slide on a smooth,circular and rigid wire frame $A$ of radius $5 \ m$ placed in a vertical plane. The wire frame is rotating about its vertical diameter at $2 \ rad/s$. When the sleeve is brought to a particular angular position $\theta$ (measured from the vertical downward axis) other than the bottom and the top of the ring,the sleeve will not slide on the wire frame. Calculate the normal force $N$ (in Newtons) of interaction between the sleeve and the wire frame at this position.

$A$ block of $200\, g$ mass moves with a uniform speed in a horizontal circular groove,with vertical side walls of radius $20\, cm$. If the block takes $40\, s$ to complete one round,the normal force by the side walls of the groove is

An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

$A$ mass of $0.5 \ kg$ is attached to a string moving in a horizontal circle with an angular velocity of $10 \ cycle/min$. Keeping the radius constant,the tension in the string is made $4$ times by increasing the angular velocity to $\omega$. The value of $\omega$ for that mass will be: