Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of θ that prevent the arrangement from collapse is

Question

Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of θ that prevent the arrangement from collapse is

Infinity Learn · Accepted Answer

W $$=$$ weight of each $$sphereN2$$ $$=$$ normal reaction between,$$4$$ and inclined $$planeN1$$ $$=$$ normal reaction between A and C $$=$$ normal reaction between B and CFree body diagram of C:Resolving vertically $$2N1cos$$ $$300$$ $$=$$ Wor $$N1=$$ $$W3-----(1)When$$ the arrangement is on the point of collapsing, the reaction between A and B is zero.Free body diagram of A:Resolving horizontally and $$verticallyN2$$ $$sin$$ θ $$=$$ $$N1sin$$ $$300$$ or $$N2sin$$ θ $$=$$ $$W23--(2)N2$$ $$cos$$ θ $$=$$ W $$+$$ $$N1$$ $$cos$$ $$300$$ $$=$$ $$3W2---(3)Dividing$$ (2) by (3) we gettan θ $$=$$ $$133$$ or θ $$=$$ $$tan$$$$-1(133)$$

Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of $θ$ that prevent the arrangement from collapse is

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