A uniform pole of length $L$ and mass $M$ is pivoted on the ground with a frictionless hinge $O$. The pole is free to rotate without friction, about a horizontal axis passing through $O$ and normal to the plane of the page. The pole makes an angle $\mathrm{\theta }$ with the horizontal. The pole is released from rest in the position shown, then the linear acceleration of the free end $P$ of the pole, just after its release would be

One end of a thin bar $AB$ of mass $m$ and length $l$ is hanging from a massless string. The other end is held at an angle of $45°$ with horizontal. Find the tension in the string, immediately after the release of the bar.

A uniform rod of length $L$ (in between the supports) and mass $m$ is placed on two supports $A$ and $B$. The rod breaks suddenly at length $\frac{L}{10}$ from the support $B$. Find the reaction at support $A$ immediately after the rod breaks.

A rigid body of radius $R$, either hollow or solid, lies on a smooth horizontal surface. The body is pulled by a horizontal force acting tangentially from the highest point. The distance travelled by the body in the time in which it makes one full rotation is the same, that it will make in one full rotation during pure rolling. The rigid body will be