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Concepts Of Physics MCQ Edition [Volume 1]PhysicsNewton's Laws of Motion

Determine the accelerations of the blocks A and B for the three situations depicted in the figure.

Options

  1. A(a) A : g 7 downward, B : 2g 7 upward (b) A : 5g 13 right, B : 10g 13 downward (c) A : g 3 downward, B : 2g 3
  2. B(a) A : 2g 7 downward, B : g 7 upward (b) A : 10g 13 right, B : 5g 13 downward (c) A : 2g 3 downward, B : g 3
  3. C(a) A : g 7 upward, B : 2g 7 downward (b) A : 5g 13 left, B : 10g 13 upward (c) A : g 3 upward, B : 2g 3 downw
  4. D(a) A : 2g 7 upward, B : g 7 downward (b) A : 10g 13 left, B : 5g 13 upward (c) A : 2g 3 upward, B : g 3 downw

Correct answer

B. (a) A : 2g 7 downward, B : g 7 upward (b) A : 10g 13 right, B : 5g 13 downward (c) A : 2g 3 downward, B : g 3

Step-by-step solution

Let T be the tension in the string for each case. For situation (a): Let the downward acceleration of block A be a . Since the string is continuous, if block A moves down by a distance x , the movable pulley (and block B ) must move up by a distance x/2 . Thus, the upward acceleration of block B is a/2 . The equations of motion are: For block A ( 4 kg ): 4g - T = 4a For block B ( 5 kg ): 2T - 5g = 5 ( a 2 ) Multiplying the first equation by 2 gives 8g - 2T = 8a . Adding this to the second equation: 8g - 5g = 8a + 5

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