Question

Find coefficient of friction \( \mu \) so that the blocks are at rest.

• A. \( \frac{1}{3} \)
• B. \( \frac{2}{3} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{1}{2} \)

Answer 1

The Correct Option is B

Concept: For a system to remain at rest in an accelerating frame, pseudo force must be considered. Pseudo force: \[ F_p = ma \] Maximum friction: \[ f = \mu N \] Step 1: Consider forces on the larger block.} Given acceleration \[ a=\frac{g}{2} \] Pseudo force on \(2\,kg\) block \[ F_p = 2 \times \frac{g}{2} = g \] Pseudo force on \(1.5\,kg\) block \[ F_p = 1.5 \times \frac{g}{2} \] Normal reaction on smaller block \[ N = \frac{1.5g}{2} \]
Step 2: Friction force.} \[ f = \mu N \] \[ f = \mu \times \frac{1.5g}{2} \]
Step 3: Apply equilibrium condition.} \[ 1.5g = g + \mu \frac{1.5g}{2} \] Divide by \(g\): \[ 1.5 = 1 + \mu \frac{1.5}{2} \] \[ 0.5 = \mu \frac{1.5}{2} \] \[ \mu = \frac{2}{3} \] Final Result \[ \mu = \frac{2}{3} \]