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A 4 kg blocks A is placed on the top of 8 kg block B which rests on a smooth table .A just slips on B when a force of 12 N is applied on B to make Both A and B move together is (4x) N Find the value of x.

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To solve the problem, we need to determine the value of \( x \) in the expression \( 4x \) N, which represents the force required to make both blocks A and B move together. ### Step-by-Step Solution: 1. **Identify the masses of the blocks:** - Mass of block A, \( m_A = 4 \, \text{kg} \) - Mass of block B, \( m_B = 8 \, \text{kg} \) 2. **Understand the condition for slipping:** - Block A slips on block B when a force of \( 12 \, \text{N} \) is applied to block B. This force represents the maximum static friction force that can act between the two blocks. 3. **Calculate the acceleration of block A:** - The force causing block A to slip is the maximum static friction force, which is \( 12 \, \text{N} \). - Using Newton's second law, \( F = m \cdot a \), we can find the acceleration \( a_A \) of block A: \[ a_A = \frac{F}{m_A} = \frac{12 \, \text{N}}{4 \, \text{kg}} = 3 \, \text{m/s}^2 \] 4. **Determine the total force required to move both blocks together:** - When both blocks A and B move together, they will have the same acceleration. The total mass of the system (A + B) is: \[ m_{\text{total}} = m_A + m_B = 4 \, \text{kg} + 8 \, \text{kg} = 12 \, \text{kg} \] - The acceleration of both blocks when a force \( F \) is applied can be expressed as: \[ F = m_{\text{total}} \cdot a \] - Substituting the values: \[ F = 12 \, \text{kg} \cdot 3 \, \text{m/s}^2 = 36 \, \text{N} \] 5. **Relate the total force to \( 4x \):** - According to the problem, the total force \( F \) is also given as \( 4x \): \[ 4x = 36 \, \text{N} \] - To find \( x \), we solve for \( x \): \[ x = \frac{36 \, \text{N}}{4} = 9 \] ### Final Answer: The value of \( x \) is \( 9 \).
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Knowledge Check

  • A block A of mass 4 kg is placed on another block B of mass 5 kg and the block rests on a smooth horizontal table. For sliding the block A on B, a horizontal force of 12 N is required to be applied on it. The maximum horizontal force that can be applied on B so that both A and B move together and the acceleration produced by this force is

    A
    25 N, 5 `m//s^(2)`
    B
    27 N, 3 `m//s^(2)`
    C
    30 N, 8 `m//s^(2)`
    D
    cannot be calculated from the given data.
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