A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is applied at a distance of $$2L/3$$ from the hinge so thatthe rod swings to the right. The reaction at the hinge is

A circular disk of radius $$'R'$$ rolls without slipping at a velocity $$v$$. The magnitude of the velocity at point $$'P'$$ (see figure) is

Consider a truss $$PQR$$ loaded at $$P$$ with a force $$F$$ as shown in the figure. The tension in the member $$QR$$ is

A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in the figure below. The coefficient of friction is $$\mu $$. If $$\mu < \tan \theta $$, then the time taken by the block to reach anorher point $$Q$$ on the inclined plane, where $$PQ=S,$$ is