Equilibrium of a particle

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Question

Three identical rigid circular cylinders A, B and C are placed on smooth inclined plane shown in the figure. The minimum value of tan $θ$ that prevent the arrangement from
collapse is $\frac{1}{3 \sqrt{n}}$ . The value of n is _________.

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Solution

$From free body diagram of cylinder A, 2 N \cos 30^{\circ} = m g$
$∴ N = \frac{m g}{\sqrt{3}}$
From free body diagram, of cylinder B,
$\begin{array}{l} N_{0} \cos θ = m g + N \cos 30^{\circ} \\ N_{0} \sin θ = N \sin 30^{\circ} \\ \tan θ = \frac{N \sin 30^{\circ}}{m g + N \cos 30^{\circ}} \end{array}$
$Putting the value of N, \tan θ = \frac{1}{3 \sqrt{3}}$
$∴ n = 3$

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Equilibrium of a particle

Remember concepts with our Masterclasses.

Three identical rigid circular cylinders A, B and C are placed on smooth inclined plane shown in the figure. The minimum value of tan θ that prevent the arrangement fromcollapse is 13n. The value of n is _________.

From free body diagram of cylinder A,2Ncos⁡30∘=mg∴ N=mg3From free body diagram, of cylinder B,N0cos⁡θ=mg+Ncos⁡30∘N0sin⁡θ=Nsin⁡30∘tan⁡θ=Nsin⁡30∘mg+Ncos⁡30∘ Putting the value of N,tan⁡θ=133∴ n=3

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free study material

Three identical rigid circular cylinders A, B and C are placed on smooth inclined plane shown in the figure. The minimum value of tan $θ$ that prevent the arrangement from
collapse is $\frac{1}{3 \sqrt{n}}$ . The value of n is _________.