JEE Advanced2017PhysicsRotational MotionActual
A rigid uniform bar A B of length L is 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 correct?
Options
- AWhen the bar makes an angle θ with the vertical, the displacement of its midpoint from the initial positi
- BThe midpoint of the bar will fall vertically downward
- CInstantaneous torque about the point in contact with the floor is proportional to sin θ
- DThe trajectory of the point A is a parabola
Correct answer
A. When the bar makes an angle θ with the vertical, the displacement of its midpoint from the initial positi
Step-by-step solution
When the bar makes an angle θ , the height of its COM (mid point) is L 2 cos θ . ∴ Displacement = L - L 2 cos θ = L 2 1 - cos θ Since, force on COM is only along the vertical direction, hence, COM is falling vertically downward. Now, x = L 2 sin θ y = L cos θ x 2 L 2 2 + y 2 L 2 = 1 Put of A is an ellipse. Torques about the point of contact, τ → = r → × F → ⇒ τ = m g L 2 sin θ