SATHEE: Rotation 1 Question 11

Rotation 1 Question 11

14. A cylinder uniform $rod$ of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the

pivot and then released. The angular acceleration of the rod when it makes an angle $θ$ with the vertical, is

(2017 Main)

(a) $\frac{2 g}{3 l} \sin θ$

(b) $\frac{3 g}{2 l} \cos θ$

(d) $\frac{3 g}{2 l} \sin θ$

Show Answer

Answer:

Correct Answer: 14. (d)

Solution:

As the rod rotates in vertical plane so a torque is acting on it, which is due to the vertical component of weight of rod.

Initial condition

At any time $t$

Now, Torque $τ =$ force $\times$ perpendicular distance of line of action of force from axis of rotation

$= m g \sin θ \times \frac{l}{2}$

Again, Torque, $τ = I α$

Where, $I =$ moment of inertia $= \frac{m l^{2}}{3}$

[Force and Torque frequency along axis of rotation

$α =$ angular acceleration passing through in end]

$∴ m g \sin θ \times \frac{l}{2} = \frac{m l^{2}}{3} α$

$∴ α = \frac{3 g \sin θ}{2 l}$

पिछला

अगला

Rotation 1 Question 11

14. A cylinder uniform $rod$ of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the

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

Rotation 1 Question 11

14. A cylinder uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the

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

Menu

14. A cylinder uniform $rod$ of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the