Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread

Question

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient of friction $μ$ . The cube (S) moves towards the right with acceleration of $\frac{g}{2}$ , where $g$ is gravitational acceleration. During this movement the block P and Q remain stationary. The value of $μ$ is ______. (Take g = 10 ${m/s}^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(2)

$From F.B.D of 1.5 kg block: f = μ N_{2} = μ \times \frac{1.5 g}{2}$ $. . . (i)$

$f + T = 1.5 g$ $. . . (i i)$

$From F.B.D of 2 kg block: T = 2 \times \frac{g}{2}$ $. . . (i i i)$

$From (i), (ii) and (iii)$

$μ \times \frac{1.5 g}{2} + 2 \times \frac{g}{2} = 1.5 g \Rightarrow μ = \frac{2}{3}$

Solution

1 0.33

2 0.67

3 1

4 0.5

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Solution

1 0.33

2 0.67

3 1

4 0.5

Ans. (2) From F.B.D of 1.5 kg block: f=μN2=μ×1.5g2 ...(i) f+T=1.5g ...(ii) From F.B.D of 2 kg block: T=2×g2 ...(iii) From (i), (ii) and (iii) μ×1.5g2+2×g2=1.5g⇒μ=23

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