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Question

Two uniform rods tied together with the help of a string are balanced as shown in the figure. The minimum coefficient of friction for which the system will remain in equilibrium in the position is 2x. The value of x is
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Solution



First balance the force in horizontal and vertical direction:
T = μNμN .... (i)
mg = N ......(ii)

From (i) and (ii) we get:
T=μmg
For the rods to be in rest the torque must be zero.
Taking torque about point 'P'.
τ=0τ=mgl2cos370Tlsin370=0mgl2cos370=Tlsin370
By putting value of T:
T=μmg

We get:
mgl2cos370=μmglsin37012cos370=μsin370μ=23
μ=23=2x

Therefore, x=3

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