A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is $\left( \mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } \right)$
(1) 0.5
(2) 0.7
(3) 0.3
(4) 0.6

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of $\_\_\_\_$ from the centre:
(1) 8 cm
(2) 4 cm
(3) 1 cm
(4) 2 cm

A block of mass m is at rest w.r.t. hollow cylinder which is rotating with angular speed $\omega$. Radius of cylinder is R. Find minimum coefficient of friction between block and cylinder.
(A) $\frac{g}{4\omega^2 R}$
(B) $\frac{3g}{2\omega^2 R}$
(C) $\frac{g}{\omega^2 R}$
(D) $\frac{2g}{\omega^2 R}$