Answer :
Answer:
[tex]m = 23.3 kg[/tex]
Explanation:
As we know that it will have constant torque on it
so the acceleration of the ball will be constant so here we can say that we can use kinematics equation
[tex]\theta = \omega_i t + \frac{1}{2}\alpha t^2[/tex]
[tex]160(2\pi) = 0 + \frac{1}{2}\alpha (15^2)[/tex]
[tex]320 \pi = 112.5 \alpha[/tex]
so we have
[tex]\alpha = \frac{320\pi}{112.5}[/tex]
[tex]\alpha = 8.94 rad/s^2[/tex]
now we know that
[tex]\tau = I \alpha[/tex]
[tex]10.8 = I(8.94)[/tex]
[tex]I = 1.21 kg m^2[/tex]
so we know that
[tex]I = \frac{2}{5}mR^2 [/tex]
here we know that
diameter = 0.72 m
so radius (R) = 0.36 m
[tex]\frac{2}{5}m(0.36^2) = 1.21[/tex]
[tex]m = 23.3 kg[/tex]