(i) A spinning disk has a hole at its centre. The surface of the disk is horizontal and a small block A of mass m = 1 kg is placed on it.

Block A is tied to a light inextensible string, other end of which passes through the hole and supports another block B of mass M = 2 kg. The coefficient of friction between A and the disk surface is 0.5. It was observed that the disk is spinning with block A remaining at rest relative to the disk. Block B was found to be stationary. It was estimated that length of horizontal segment of the string (r) was anywhere between 1.0 m to 1.5 m. With this data what estimate can be made about the angular speed `(omega)` of the disk. `[g = 10 m//s^(2)`] (ii) A spring has force constant equal to `k = 100 Nm^(–1)`. Ends of the spring are joined to give it a circular shape of radius R = 20 cm. Now the spring is rotated about its symmetry axis (perpendicular to its plane) such that the circumference of the circle increases by `1%`. Find the angular speed `(omega)`. Mass of one meter length of the spring is `lambda = 0.126 gm^(–1)`.

Answer

(i) `sqrt(15) lt omega sqrt(16.67) "rad"//"s"`
(ii) `500 "rad"s^(-1)`