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A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal line passing through A . If the cable at B breaks then just after that the angular acceleration of the plate is

Options

  1. A3 g 2 2 b
  2. B3 g 2 b
  3. Cg 2 b
  4. D2 g 3 b

Correct answer

A. 3 g 2 2 b

Step-by-step solution

The plate will rotate about the hinged point ( point A ) after breaking of the cable ∴ using τ = Iα for the plate Mg b 2 = 2 3 Mb 2 α ( Moment of inertia about point A is Mb 2 6 + M b 2 2 = 2 3 Mb 2 ) ∴   α = 3 g 2 2 b

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