Question:
A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4\, \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ Ma ^{2} \Omega}{48}\right) n$. The value of $n$ is ______
A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4\, \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ Ma ^{2} \Omega}{48}\right) n$. The value of $n$ is ______
Updated On: May 22, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 49
Solution and Explanation
Answer: 49
Was this answer helpful?
0
0
Top Questions on rotational motion
- A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is \( F \) and the angular velocity of the tube is \( \omega \), then the value of \( \alpha \) is _______ in SI units.
- JEE Main - 2025
- Physics
- rotational motion
- A uniform rod AB of length 1 m and mass 4 kg is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the rod A and Bare 3 m/s and 4 m/s respectively, as shown in the figure. Then which of the following statement(s) is/are correct?
- WBJEE - 2024
- Physics
- rotational motion
- The position vector of a particle of mass \(m\) moving with a constant velocity \(\mathbf{u}\) is given by \(\mathbf{r} = x(t)\hat{i} + b\hat{j}\), where \(b\) is a constant. At an instant, \(\mathbf{r}\) makes an angle \(\theta\) with the x-axis as shown in the figure. The variation of the angular momentum of the particle about the origin with \(\theta\) will be:
- WBJEE - 2024
- Physics
- rotational motion
- A small ball of mass m is suspended from the ceiling of a floor by a string of length L. The ball moves along a horizontal circle with constant angular velocity Ο, as shown in the figure. The torque about the center (O) of the horizontal circle is:
- WBJEE - 2024
- Physics
- rotational motion
- Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is \(\sqrt\frac{8} {x }\). The value of x is:
- JEE Main - 2024
- Physics
- rotational motion
View More Questions
Questions Asked in JEE Advanced exam
- Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance \(d (βͺ a)\) between them, as shown in the figure. Let \(C_0 = \epsilon_0\frac{a^2}{d}, \)where \(\epsilon_0\) is the permittivity of free space.
Match the quantities mentioned in List-I with their values in List-II and choose the correct option.List-I List-II P The capacitance between S1 and S4, with S2 and S3 not connected, is I \(3C_0\) Q The capacitance between S1 and S4, with S2 shorted to S3, is II \(\frac{C_0}{2}\) R The capacitance between S1 and S3, with S2 shorted to S4, is III \(\frac{C_0}{3}\) S The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is IV \(2\frac{C_0}{3}\) \[2C_0\] - JEE Advanced - 2024
- Moment Of Inertia
- A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle \(\theta\) at P, as shown in the figure. When \(\theta = 30\) , then the electric flux through the curved surface of the cylinder is \(Ξ¦\). If \(\theta= 60\degree\) , then the electric flux through the curved surface becomes \(Ξ¦/βπ\), where the value of n is______.
- JEE Advanced - 2024
- Electric Flux
- Let \(\frac{\pi}{2}<x<\pi\) be such that \(\cot x=\frac{-5}{\sqrt{11}}\). Then
\((\sin\frac{11x}{2})(\sin 6x-\cos6x)+(\cos\frac{11x}{2})(\sin 6x+\cos 6x)\)
is equal to- JEE Advanced - 2024
- Trigonometric Identities
- A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field π΅β pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height πΏ, is placed in the x-y plane with its vertex P at x = 0 in the orientation shown in the figure. At π‘ = 0, the loop starts entering the region of the magnetic field with a uniform velocity π£ along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (π₯) starting from π₯ = 0? - Let R2 denote R Γ R. Let
S = {(a, b, c) : a, b, c β R and ax2 + 2bxy + cy2 > 0 for all (x, y) β R2 - {(0, 0}}.
Then which of the following statements is (are) TRUE ?- JEE Advanced - 2024
- Quadratic Equations
View More Questions
Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)