Two balls of mass `m_(1) = 56g` and `m_(2) = 28g` are suspended on two threads of length `l_(1) = 7 cm` and `l_(2) = 11 cm` at the end of a freely hanging rod (Fig). Determine the angular velocity o at which the rod should be rotated about the vertical axle so that it remains in the vertical position.

A uniform thin rod of length l and mass m is hinged at a distance l//4 from one of the end and released from horizontal position as shown in Fig. The angular velocity of the rod as it passes the vertical position is

A uniform thin rod of length l and mass m is hinged at a distance l//4 from one of the end and released from horizontal position as shown in Fig. The angular velocity of the rod as it passes the vertical position is

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 angle will the rod make with the vertical

A conical pendulum, a thin uniform rod of length l and mass m , rotates uniformly about a vertical axis with angular velocity omega (the upper end of the rod is hinged). Find the angle theta between the rod and the vertical.

Two balls of masses m_(1)=100 g and m_(2)=300 g are suspended from point A by two equal inextensible threads, each of length l=32/35m . Ball of mass m_(1) is drawn aside and held at the same level as A but at a distance (sqrt(3)/2)l from A , as shown in Fig. When ball m_(1) is released, it collides elastically with the stationary ball of mass m_(2) . Velocity u_(1) with which the hall of mass m_(1) collides with the other ball is

A homogenous rod XY of length L and mass 'M' is pivoted at the centre 'C' such that it can rotate freely in vertical plane. Initially the rod is in the horizontal position.