In the arrangement shown in the figure, the rod and the sleeve have friction coefficient of 1/3. The mass of the hanging block is 2 kg. The sleeve is just on the verge of sliding down. What is the mas

Question

In the arrangement shown in the figure, the rod and the sleeve have friction coefficient of 1/3. The mass of the hanging block is 2 kg. The sleeve is just on the verge of sliding down. What is the mass (in kg) of the sleeve.

TestHub · Accepted Answer

Tension in the string: T = 2 g = 20 N Horizontal force on the sleeve (rod is at 3 7 ∘ ): N = T sin 3 7 ∘ = 20 × 5 3 ​ = 12 N Sleeve is on the verge of sliding down, so friction acts up: T cos 3 7 ∘ + μ N = m g 20 × 5 4 ​ + 3 1 ​ × 12 = 10 m 16 + 4 = 10 m ⇒ m = 2 kg

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