A circular tube of radius R and cross-sectional radius r ( r R ) is filled completely with iron balls of the radius ρ . Iron balls are just fitting into the tubes. The tension in the tube when it is rotated about its axis perpendicular to its plane with angular velocity ω

Question

A circular tube of radius R and cross-sectional radius r ( r R ) is filled completely with iron balls of the radius ρ . Iron balls are just fitting into the tubes. The tension in the tube when it is rotated about its axis perpendicular to its plane with angular velocity ω, 4 3 π ρ ω 2 r 3 R, 4 3 π ρ ω 2 r 2 R 2, 2 3 π ρ ω 2 r 3 R, 2 3 π ρ ω 2 r 2 R 2

MARKS App · Accepted Answer

∵ r R , m a s s / l e n g t h can be given by λ = m 2 r = 4 3 πr 3 ρ 2 r = 2 3 π r 2 ρ Now, Tension in the tube is given by T = λ . ω 2 R R = 2 3 π r 2 ρ ω 2 R . R = 2 3 π ρ ω 2 r 2 R 2

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