Question

A 5 × 10–6-kg dot of paint on the side of a rotating cylinder flies off when the angularspeed of the cylinder reaches 5 × 103 rad/s. The spin axis of the cylinder is vertical andits radius is 0.04 m. The force of adhesion between the paint and the surface isapproximatelyA) 1 NB) 1 mNC) 5 mND) 5 kNE) 5 N

Answer 1

E) 5 N

Step-by-step explanation:

The dot of paint on the side of the rotating cylinder experiences an pseudo force called centrifugal force in radially outward direction.

The centrifugal force on a rotating body of mass m, angular velocity w and radius r is given by the expression.

Centrifugal force,

`F=mrw^(2)`

When this centrifugal force F just exceeds adhesive force between the paint and the surface the dot flies off.

from the question we get the value angular velocity at which the dot flies of as
`5X10^(3)`

we have,

`m= 5 X10^(-6)`

r = 0.04 m

therefore the centrifugal force at this point,

F = mr
`w^(2)`

=
`(5X10^(-6) ) X (5X10^(3) )^(2) X0.04`

= 125 X 0.04

= 5 N

so, Adhesive force or Adhesion = 5 N