SATHEE: Rotation 5 Question 12

Rotation 5 Question 12

22. 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/are correct?

(2017 Adv.)

(a) Instantaneous torque about the point in contact with the floor is proportional to $\sin θ$

(b) The trajectory of the point $A$ is parabola

(d) When the bar makes an angle $θ$ with the vertical, the displacement of its mid-point from the initial position is proportional to $(1 - \cos θ)$

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Answer:

Correct Answer: 22. (a,c,d)

Solution:

When the bar makes an angle $θ$ , the height of its COM (mid-point) is $\frac{L}{2} \cos θ$ .

$∴$ Displacement $= L - \frac{L}{2} \cos θ = \frac{L}{2} (1 - \cos θ)$

Since, force on COM is only along the vertical direction, hence COM is falling vertically downward. Instantaneous torque about point of contact is

$τ = m g \times \frac{L}{2} \sin θ$

$τ \propto \sin θ$

Now,

$\begin{aligned} x & = \frac{L}{2} \sin θ \\ y & = L \cos θ \\ \frac{x^{2}}{(L / 2)^{2}} + \frac{y^{2}}{L^{2}} & = 1 \end{aligned}$

Path of $A$ is an ellipse.

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Rotation 5 Question 12

22. 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/are correct?

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Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

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नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Rotation 5 Question 12

22. A rigid uniform bar AB 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/are correct?

Matching Type Questions

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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22. 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/are correct?