A uniform L shaped rod each of side a is held ,as shown in the figure. The angle `theta` such that rod remains stable. Will be.

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

Two identical thin uniform rods of length L each are joined to form T shape as shown in the figure. The distance of centre of mass from D is

A uniform rod of length L pivoted at the bottom of a pond of depth L//2 stays in stable equilibrium as shown in the figure. Find the angle 0 if the density of the material of the rod is half of the density of water.

Four identical heat conductors are connected as shown in the figure. The temperature theta of the junction is [rods are insulated from the sides ]

A rod of mass m and length l is rotating about a fixed point in the ceiling with an angular velocity omega as shown in the figure. The rod maintains a constant angle theta with the vertical. What will be the horizontal component of angular momentum of the rod about the point of suspension in terms of m , omega , l and theta .

A rod of length 2l is bent as shown in figure. Coordinates of centre of mass are

A smooth rod length l is kept inside a trolley at an angle theta as shown in the figure. What should be the acceleration a of the trolley so that the rod remain in equilibrium with respect to it?

In the figure shown S is a large nonconducting sheet of uniform charge density sigma . A rod R of length l and mass 'm' is parallel to the sheet and hinged at its mid point. The linear charge densities on the upper and lower half of the rod are shown in the figure. Find the angular acceleration of the rod just after it is released.