A uniform stick of length `l` is mounted so as to rotate about a horizontal axis perpendicular to the stick and at a distance `d` from the centre of mass. The time period of small oscillation has a minimum value when `d//l` is

A uniform stick of length l is hinged so as to rotated about a harmonic axis perpendicular to the stick, at a distance from the center . Find the value of x, for which the time period is minimum.

A uniform stick of length l is hinged so as to rotated about a harmonic axis perpendicular to the stick, at a distance from the center . Find the value of x, for which the time period is minimum.

The radius of gyration of a uniform rod of mass m and length l about an axis perpendicular to its length and at distance l/4 from its centre will be

A uniform rod of mass m , length l rests on a smooth horizontal surface. Rod is given a sharp horizontal impulse p perpendicular to the rod at a distance l//4 from the centre. The angular velocity of the rod will be

A uniform rod of mass m , length l rests on a smooth horizontal surface. Rod is given a sharp horizontal impulse p perpendicular to the rod at a distance l//4 from the centre. The angular velocity of the rod will be

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 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.