Circular Motion Questions

A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speed $v_A$ and $v_B$ respectively. Their time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be:

A block of mass $10\text{kg}$ is in contact against the inner wall of a hollow cylindrical drum of radius $1\text{m}$. The coefficient of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ($g=10{\text{m/s}}^2$)

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig. $y$ -projection of the radius vector of rotating particle $P$ is:

A particle starting from rest moves in a circle of radius $r$. It attains a velocity of $v_0\text{m/s}$ on completion of $n$ rounds. Its angular acceleration will be: