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MHT CET202415 May 2024Morning ShiftPhysicsRotational MotionActual

A thin uniform metal rod of mass ' M ' and length ' L ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' '. Its centre of mass rises to a maximum height of ( g = Acceleration due to gravity)

Options

  1. AL ^2 ^2 3 ~g
  2. BL^2 ^2 2 g
  3. CL ^2 ^2 6 ~g
  4. DL ^2 ^2 4 ~g

Correct answer

C. L ^2 ^2 6 ~g

Step-by-step solution

By conservation of energy, 1 2 I ^2= Mgh h = I ^2 2 Mg = h ...(i) The M.I of a uniform rod about an axis passing through its centre is ML ^2 12 . As the axis passing through the end, using parallel axis theorem, I = ML ^2 12 + M ( ~L 2 )^2= ML ^2 3 ...(ii) Putting (ii) into (i), h= L^2 ^2 6 g

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