A rod of length R and mass M is free to rotate about a horizontal axis passing through hinge P as in figure.First it is taken aside such that it becomes horizontal and then released.At the lowest point the rod hits the block B of mass m and stops.The value of `((M)/(m))^(2)` such that the block B completes the circular track of radius R is (Neglect any friction)

A thin bar of mass M and length L is free to rotate about a fixed horizontal axis through a point at its end. The bar is brought to a horizontal position and then released. The axis is perpendicular to the rod. The angular velocity when it reaches the lowest point is

A uniform rod of mass m is rotated about an axis passing through point O as shown. Find angular momentum of the rod about rotational law.

A uniform rod of length L and mass m is free to rotate about a frictionless pivot at one end as shown in figure. The rod is held at rest in the horizontal position and a coin of mass m is placed at the free end. Now the rod is released The reaction on the coin immediately after the rod starts falling is

A unifrom rod of length l and mass m is free to rotate in a vertical plane about A as shown in Fig. The rod initially in horizontal position is released. The initial angular acceleration of the rod is

A metallic rod of mass m length R is pivoted at O. It is free to rotate about a horizontal axis passing through O . An inward magnetic field is applied as shown in the figure. Find the ratio of maximum electric field inside the metallic rod to the applied magnetic field induction .

Moment of inertia of a rod of mass M and length L about an axis passing through a point midway between centre and end is

A uniform rod of length 4l and mass m is free to rotate about a horizontal axis passing through a point distant l from its one end. When the rod is horizontal its angular velocity is omega as shown in figure. calculate (a). reaction of axis at this instant, (b). Acceleration of centre of mass of the rod at this instant. (c). reaction of axis and acceleration of centre mass of the rod when rod becomes vertical for the first time. (d). minimum value of omega , so that centre of rod can complete circular motion.

A thin uniform rod is free to rotate about a fixed smooth horizontal axis as shown. A point mass hits horizontally with velocity v_(0) to the one end B of the rod. When it hits, it sticks to the rod, then :

A slender rod of mass m and length L is pivoted about a horizontal axis through one end and released from rest at an angle of 30^@ above the horizontal. The force exerted by the pivot on the rod at the instant when the rod passes through a horizontal position is