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

Consider the arrangement displayed in the figure. The pulleys and the string are light, and all surfaces are frictionless. Determine the acceleration of the mass M .

Options

  1. A2g 3
  2. Bg 3
  3. Cg 2
  4. D4g 3

Correct answer

A. 2g 3

Step-by-step solution

Let T be the tension in the string. For the hanging mass M moving downwards with acceleration a , the equation of motion is: Mg - T = Ma The movable pulley B is pulled towards the right by two segments of the string. The net force on the block of mass 2M is 2T . Let its acceleration be a_B . The equation of motion is: 2T = 2M a_B T = M a_B Using the string constraint, if pulley B moves to the right by a distance x , both horizontal segments of the string shorten by x , releasing a total length of 2x . Thus, mass M

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