Blocks A and B mass 5 kg and 3kg are connected by a light inextensible string passing under a smooth light pulley C which carries a particle D of mass 4 kg. A and B rest on a horizontal rough surfaces as shown in the diagram. The coefficient of friction is same for both A and B and is just sufficient to prevent A but not B, from moving. Find the coefficient of friction.

Answer

`mu = (6)/(17)`

Explanation

F.B.Ds of all four bodies are shown
From constraint relation, acceleration of 3kg
block is twice of acceleration of 4 kg block.
so `4g -2T =4a` …(i)
`T -3 mug = 3 xx 2a`….(ii)
also `T = 5 mu g`....(iii)
`rArr` (i) and (ii)
`4g - 6 mug = 4a + 12a`
`rArr a = ((4 - mu 6)g)/(16)`
by (i)
`4g -4T=(4xx4mu6g)/(16)`
`rArr 4g -2T =g -(3)/(2) mug`
`rArr T=(3)/(2)8 +(3)/(4) mu g = 5 mug`
`(3)/(2)=mu(5-(3)/(4))=(17 mu)/(4)rArr mu =(6)/(17)`.