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 - from rest under a constant torque - 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

The correct option is C t = 2m ( a^2+2r^2 )ω/τL = τ t ⇒ t = 4 ( mr^2+1/2ma^2 )ω/τ ⇒ t = 2m ( a^2+2r^2 )ω/τ ...

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Byju's Answer

Standard X

Physics

Newton's Second Law: Rotatory Version

A centrifuge ...

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

t = \frac{4 m r^{2} ω}{τ}

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t = \frac{2 m (a^{2} + 2 r^{2}) ω}{τ}

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t = \frac{2 m a^{2} ω}{τ}

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t = \frac{2 m (r^{2} + 2 a^{2}) ω}{τ}

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Solution

The correct option is B $t = \frac{2 m (a^{2} + 2 r^{2}) ω}{τ}$
$L = τ t$
$\Rightarrow t = \frac{4 (m r^{2} + \frac{1}{2} m a^{2}) ω}{τ}$
$\Rightarrow t = \frac{2 m (a^{2} + 2 r^{2}) ω}{τ}$

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

The correct option is B $t = \frac{2 m (a^{2} + 2 r^{2}) ω}{τ}$
$L = τ t$
$\Rightarrow t = \frac{4 (m r^{2} + \frac{1}{2} m a^{2}) ω}{τ}$
$\Rightarrow t = \frac{2 m (a^{2} + 2 r^{2}) ω}{τ}$