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Question

# A centrifuge consists of four solid cylindrical containers, each of mass 'm' at radial distance 'r' from the axis of rotation. A time 't' is required to bring the centrifuge to an angular velocity ω from rest under a constant torque τ applied to the shaft. The radius of each container is 'a' and the mass of the shaft and the supporting arms is small compared to 'm'. Then

A
t=4mr2ωτ
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B
t=2m(a2+2r2)ωτ
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C
t=2ma2ωτ
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D
t=2m(r2+2a2)ωτ
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Solution

## The correct option is B t=2m(a2+2r2)ωτL=τt ⇒t=4(mr2+12ma2)ωτ ⇒t=2m(a2+2r2)ωτ

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