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When a mass M is placed in a centrifuge that is rotating at w rad/s and if r is the radius of the centrifuge, the centrifugal force on the mass is equal to F = M*w^2*r. The maximum mass that can be held in the centrifuge is equal to a value M where the centrifugal force acting on the mass Mw^2r is equal to the tensile strength.
In the problem the radius of the centrifuge is 0.06 cm = 0.0006 m and the angular velocity is 24000 rpm = `(24000*2*pi)/60` = 2513.27 rad/s.
The centrifugal force acting on a mass M is M*2513.27^2*0.0006. Equating this to the tensile strength 1200 N gives:
M*2513.27^2*0.0006 = 1200
=> `M = 1200/(2513.27^2*0.0006)`
=> `M ~~ 0.32` kg
The maximum mass that the centrifuge can hold given the tensile strength is 0.32 kg.
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