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Q.

Two blocks each of mass 1 kg are placed as shown. They are connected by a string which passes over a smooth (massless) pulley. There is no friction between m₁ and the ground. The coefficient of friction between m₁ and m₂ is 0.2. A force F is applied to m₂. Which of the following statements is/are correct? (Use $g = 10 m s^{- 2}$ )

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a

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

b

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

c

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

d

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

answer is A, C, D.

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Detailed Solution

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

In critical case T = 2N, F = T + 2 = 4N

$∴$ System is in equilibrium if $F \leq 4 N$

For $F > 4 N$

$F - (T + 2) = m_{2} a = (1) (a) \dots . . (i)$

$T - 2 = m_{2} a = (1) (a) \dots . . (i i)$

On solving two equations, we get $T = \frac{F}{2}$

When F = 6N, T = 3N

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