A disc of metal of raidus r with its plane vetical can be made to swing about a horiziontal axis passsing through any one of a series of holes bored along a diameter. Show that the minimum period of oscillatin is given by `t=2pi sqrt(1.414r)/(g)`

A uniform circular disc of mass m and radius a,can rotate in a vertical plane about a horizontal axis through a point O on its circumference.The disc is held with the diameter OA through O horizontal and then released. If a constant frictional couple of (mga)/(2 pi) opposes the motion, the angular speed when OA is vertical will be 1) sqrt(g/2a) 2) sqrt(g/a) 3) sqrt(g/3a) 4) sqrt(2g/3a)

An annular ring of internal and outer radii r and R respectively oscillates in a vertical plane about a horizontal axis perpendicular to its plane and passing through a point on its outer edge. Calculate its time period and show that the length of an equivalent simple pendulum is (3R)/(2) as r rarr 0 and 2 R as r rarr R .

Two identical uniform thin rods have been connected at right angles to form a ‘T’ shape. One end of a rod is connected to the centre of the other rod. Length of each rod is L. The upside down ‘T’ can swing like a pendulum about a horizontal axis passing through the top end (see fig.). Axis is perpendicular to plane of the fig. The speed of the meeting point of the two rods is u = 2 sqrt(gL) when it is at its lowest position. Calculate the angular acceleration of the ‘T’ shaped object when it is at extreme position of its oscillation.

A disc of mass m and radius R is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass m//2 each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity omega_(0) and released. The angular speed of the disc when the balls reach the end of the disc is

A disc of mass m and radius R is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass m//2 each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity omega_(0) and released. The net work done by forces exerted by the disc on the ball for the duration ball remains on the disc is

A disc of mass m and radius R is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass m//2 each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity omega_(0) and released. The speed of each ball relative to the ground just after they leave the disc is