A steel ball of mass 2.4 kg is tied to a string and whirled it in a horizontal plane in a circle of diameter 2 m at a constant speed of 20 rpm. The tension in the string is (ignore gravity)

Concept:

Tension in the string = centrifugal force developed due to circular motion

T = mrω²

where T = tension in the string, m = mass of the ball, ω = angular velocity of rotation, r = radius of the circle of rotation

Angular velocity \(ω = \frac{{2π N}}{{60}}\)

where N is the speed in rpm.

Calculation:

Given:

m = 2.4 kg, Speed (N) = 20 rpm, diameter of circle of rotation (d) = 2 m, so radius of circle of rotation (r) = 1 m

angular speed of rotation \(ω = \frac{{2π N}}{{60}}\)

\(ω = \frac{{2π~ ×~20}}{{60}}\)

ω = 2.094 rad/sec

Now Tension T = 2.4 × 1 × 2.094²

T = 10.52 N