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Block B of mass m(B) = 0.5 kg rests on b...

Block B of mass `m_(B) = 0.5 kg` rests on block A, with mass `m_(A) = 1.5kg` which in turn is on a horizontal tabletop (as shown in figure) .The coefficient of kinetic friction between block A and the tabletop is `mu_(k) = 0.4` and the coefficient of static friction between block A and blockB is `mu_(s) = 0.6` A light string attached block A passes over a frictionless, massless pulley and block C is suspended from the other end of the string. What is the largest mass `m_(c)` (in kg) that block C can have so that block A and B still slide together when the system is replaced from rest?

Text Solution

Verified by Experts

The correct Answer is:
5
Denote the common magnitude of the maximum acceleration as a For block A as remain at rest with repect to block B , `ale mu_(s)g` Let as assume `a = m_(s)g` for mass C in the largest The tension in the cord is then
`T = (m_(A) + m_(B)) a + mu_(k)g(m_(A) + m_(B))`
`= (m_(A) + m_(B)) (a + mu_(k)g)`
The tension is relted to the mass `m_(c)` (largest by)
`T = m_(C) (g - d)`
Solving `m_(c)` yiclds
`m_(c) = ((m_(A) + m_(B))(mu_(s) + mu_(k)))/(1 - mu_(s))`
`= ((0.5 + 0.5)(0.6 +0.4))/(1 - 0.6)= 5kg`
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Knowledge Check

  • In the arrangement shown in figure coefficient of friction between 5kg block and incline plane is mu=0.5 . Friction force acting on the 5kg block is

    A
    `20 N`
    B
    `15N`
    C
    `10 N`
    D
    `5 N`

  • A block of mass m=4kg is placed oner a rough inclined plane as shown in figure. The coefficient of friction between the block and the plane is mu=0.5 . A force F=10N is applied on the block at an angle of 30^(@) .

    A
    static in nature in the direction up the plane and have the value `30.2N`
    B
    static in nature in the direction down the plane and have the value `30.2N`
    C
    kinetic in nature in the direction up the plane and have the value `30.2N`
    D
    None of these

  • Block B rests on a smooth surface .The coefficient of static friction between A and B is mu = 0.4 where F = 30 N then Acceleration of upper block is

    A
    `3//2 ms^(-2)`
    B
    `6//7 ms^(-2)`
    C
    `4//3 ms^(-2)`
    D
    `3//7 ms^(-2)`