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AP EAMCET20227 Jul 2022Evening ShiftPhysicsRotational MotionActual

A uniform rod of length 60 ~cm is placed with one end in contact with the horizontal table and is then inclined at an angle 30^ to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is (acceleration due to gravity =10 ~ms ⁻² )

Options

  1. A9 rad s ⁻¹
  2. B6 rad s ⁻¹
  3. C5 rad s ⁻¹
  4. D8 rad s ⁻¹

Correct answer

C. 5 rad s ⁻¹

Step-by-step solution

( As rod falls, its loss of gravitational potential energy appears as gain of angular rotational energy. If rod is rotating at angular speed when it is horizontal then, Rotational K E = Loss of gravitational PE 1 2 I ^2=m g h Now for rod, Moment of inertia of a solid rod about its one end, I= M L^2 3 and h= l 2 (see figure =30^ ) = l 2 1 2 = l 4 So from eq. (i), we have 1 2 M l^2 3 ^2=M g l 4 ^2= 3 2 g l Here, g=10 ~m / s ^2 and l=0.6 ~m So, ^2= 3 2 10 0.6 =25 or =5 rad / s

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