A disc is rotatin g aro u n d its cen tre in a horizontal plane at the rate of 60 rotation/ minute. A coin `(1A^(st))` is placed at a distance of 18 cm and `2^(nd)` similar coin 20 cm from its centre. The co-efficient of static friction between the disc and the coins is 0.2. Which coin will be thrown away from the disc ? Which coin will keep rotating with the disc ?

Options

A. both coins thrown away
B. 2nd coin keep rotating 1st coin thrown away
C. both coins keep rotating
D. 1st coin keep rotating 2nd coin thrown away

Answer

A

Explanation

Suppose mass of each coin m
for the circular motion centrifugal force `le ` maximum static friction.
`(mv^(2))/(r ) le f _(s)`
Time required for 60 rotation is 60 second Time required for 1 rotation is
`T = (60)/( 60)=1`
Now linear velocity `v=(2pi r)/( T )` and `f_(s(max)) = mu_(s ) N = mu_(s ) mg`
from equation (1)
`(m )/(T) xx (2pi r)/(T ) le mu_(s ) mg`
`le ((0.2).(10).(1)^(2))/(4xx 10)`
`le 0.05 m`
`r le m`
both the coin from the 18 cm and 20 cm distance from the centre are thrown away .