The time taken for the wave on the string to travel from the centre of the circle of the ball is 6.5 * 10⁻⁶ s.
Given that, mass of the ball mb = 18.1 kg
Angular speed of the ball ω = 12.5 rad/s
Mass of the string ms = 0.0184 kg
Speed of the wave of the string is given by the formula,
sw = √(Ts / m') -------(1)
where, Ts is tension in the string
m' is mass per unit length of the strength
Ts = mb * ω² * l --------(2)
m' = ms/l ---------(3)
Substituting (2) and (3) in (1), we have
sw = √(mb * ω²* l²/ ms) ----(4)
We know that, t = l / sw -----(5)
Substituting (4) in (5), we have
t = √( ms/ mb *ω²) = √( 0.0184/(18.1 * 12.5²)) = √( 0.0184/2828.125)
= 0.0000065 = 6.5 * 10⁻⁶ s
Thus, the time taken for the wave on the string to travel from the centre of circle to the ball is 6.5 * 10⁻⁶ s.
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