Moment of inertia of a ring of radius $R$ whose mass per unit length varies with parametric angle $\theta$ according to relation $\lambda ={\lambda }_0{\cos }^2\theta$, about its axis will be

A solid hemisphere $\left(m,R\right)$ has the moment of inertia about axis $1$ (Diameter of hemisphere)

A square plate is of mass $M$ and length of edge equal to $2a$. Its $MI$ about its centre of mass axis, perpendicular to its plane is equal to $I_0$. Four identical disks are cut from the plane. The $MI$ of leftover square about same axis is

A uniform bar of mass $\mathrm{m}$ is being moved on a smooth horizontal plane by applying a constant horizontal force $F$ acting at the lowest point. If the rod translates making a constant angle $\theta$ with vertical, the value of $F$ must be

A disc of radius $R$ has linear velocity $v$ and angular velocity $\omega$ as shown in the figure. Given $v=R\omega$. Find speed of points $A,B,C,D$ on the disc.

A wheel rolls purely on ground. If the velocity of a point '$P$' as shown on periphery of a body has a velocity equal to the velocity of the centre of mass of the body. Then $\theta =$?