Question

A coin kept with it's centre at a distance of 9 cm from the axis of rotation of a disc starts slipping off when the disc speed reaches 60 r.p.m. Up to what speed the coin will remain on the disc if its centre is 16 cm from the axis of rotation of the disc?​

Answer 1

speed of the disc in radian/sec=60/60=1radian/sec

when,the coin is at distance of .09m,then upto velocity 1radianper sec ,,it is able to reamin at same position

it means that

it's maximum,static friction(umg)=

$m {w}^{2}r$

where,u is the coeeficient of static friction,,,w is the angular velocity and r is the distance of coin from the centre

now ,here

$umg = m {w}^{2}r \\ umg = m \times {1}^{2} \times .09..............i)$

now,when the coin is at 16,cm from axis of rotation

let the maximum velocity be w

$umg = m {w}^{2}r \\ umg = m {w}^{2} \times .16..................ii)$

dividing equation i) from ii) we get

$\frac{umg}{umg} = \frac{.09m}{.16m {w}^{2} } \\ = > 1 = \frac{9}{16 {w}^{2} } \\ w = \sqrt{ \frac{9}{16} } = \frac{3}{4} = 0.75radian \: per \: sec.$

{hope it helps you friend}