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99 Percentile Qs Bank for JEE MainPhysicsRotational Motion

A rectangular plate of length L , width B and mass M rotates with angular velocity ω about an axis in the x - y plane. The axis of rotation passes through the centre of the mass and cuts the length of the plate at an acute angle θ . Find total angular momentum of the plate about center of mass.

Options

  1. AM ω 12 L 2 sinθ i ^ + B 2 cosθ j ^ ω
  2. BM ω 13 B 2 cosθ i ^ + L 2 sinθ j ^
  3. CM ω 12 L 2 sin 2 θ i ^ + B 2 cos 2 θ j ^
  4. DM ω 12 B 2 cos 2 θ i ^ + L 2 sin 2 θ j ^

Correct answer

A. M ω 12 L 2 sinθ i ^ + B 2 cosθ j ^ ω

Step-by-step solution

The angular velocity is given by, ω → = ω x   i ^ + ω y   j ^ + ω z   k ^ Where ω x = ωsinθ , ω y = ωcosθ and ω z = 0 . L x = I x ω x = M L 2 12 ωsinθ L y = I y ω y = M B 2 12 ωcosθ L z = 0 L → = L x i ^ + L y j ^ + L z k ^ = M ω 12 L 2 sinθ i ^ + B 2 cosθ j ^

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