$A$ motor of an engine rotates at an angular speed of $100 \ rpm$ about its axis. When the switch is turned off,it comes to rest in $15 \ s$. How many rotations does it complete before coming to rest?

$A$ hoop of radius $r$ and mass $m$ rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side length $d$. The ratio $I_{0} / I_{A}$ of the moment of inertia $I_{0}$ of the system about an axis passing through the centroid and perpendicular to the plane of the triangle,to the moment of inertia $I_{A}$ about an axis passing through the center of any one of the spheres and perpendicular to the plane of the triangle,is:

$A$ uniform rod of length $l$ and density $\rho$ is revolving about a vertical axis passing through its one end. If $\omega$ is the angular velocity of the rod,then the centrifugal force per unit area of the rod is

The moment of inertia of a rectangular plate about an axis passing through $P$ and perpendicular to the plate is $I$. Then,the moment of inertia of the triangular portion $PQR$ about an axis perpendicular to the plane of the plate and passing through $P$ is:

$A$ rod of length $1\,m$ is standing vertically. When its upper end is released and it falls such that the lower end touches the ground without slipping,the speed of the upper end when it hits the ground is: