As we know that weight of the hanging mass will be same as tension in the string
so we will have
[tex]T = Mg[/tex]
now also we know that stopper will revolve in the circle with constant speed and the tension force will be the centripetal force on it
[tex]T = m\omega^2 R[/tex]
now we will have
[tex]Mg = m\omega^2 R[/tex]
[tex]M(9.8) = 0.05(\frac{2\pi}{0.25})^2(0.4)[/tex]
[tex]M(9.8) = 12.63[/tex]
[tex]M = 1.3 Kg[/tex]
so mass will be 1.2 kg
