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Two blocks each of mass 1kg are placed as shown. They are connected by a string which passes over a smooth (massless) pulley. There is no friction between $m_{1}$ and the ground. The coefficient of friction between $m_{1}$ and $m_{2}$ is 0.2. A force F is applied to $m_{2}$ . Which of the following statements is/are correct?

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The system will be in equilibrium if $F \leq 4 N$

If $F > 4 N$ tension in the string will be $4 N$

If $F > 4 N$ the frictional force between the blocks will be $2 N$

If $F = 6 N$ tension in the string will be 3N

answer is A, C, D.

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Detailed Solution

Maximum value of friction between two blocks

$f_{\max} = 0.2 \times 1 \times 10 = 2 N$

In critical case,

$T = 2 N F = T + 2 = 4 N$

$∴$ System is in equilibrium, if

$F - (T + 2) = m_{2} a = (1) (a)$

$T - 2 = m_{1} a = (1) (a)$

Solving these two equations, we get

$T = \frac{F}{2}$

Where F = 6N, T = 3N

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