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Q.

A rigid uniform bar AB of length L slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is θ . Which of the following statements about its motion is/are correct?

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a

Instantaneous torque about the point in contact with the floor is proportional to sinθ

b

The trajectory of the point A is a parabola

c

The midpoint of the bar will fall vertically downward

d

When the bar makes an angle θ with the vertical, the displacement of its midpoint from the initial position is proportional to 1−cosθ.

answer is A.

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Detailed Solution

rB=mgℓ2sin⁡θ⇒ Option [A] is correct. [B] Coordinates of point A , x=L2sin⁡θ and y=Lcos⁡θ⇒2xL2+yL2=1 This represents ellipse. Since, there is no external force in horizontal direction, option [C] is correct. ΔXcom=ℓ2−ℓ2cos⁡θ=ℓ2(1−cos⁡θ)⇒ Option [D] is correct.

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