Question:
A particle performing uniform circular motion has angular momentum $L$. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
A particle performing uniform circular motion has angular momentum $L$. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
Updated On: Jul 5, 2022
- $L/4$
- $4L$
- $2L$
- $L/2$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Angular momentum of a particle performing uniform circular motion
$L = I?$
Kinetic energy, $K=\frac{1}{2}\omega^{2}$
Therefore, $L=\frac{2K}{\omega^{2}}\omega=\frac{2K}{\omega}$
$\frac{L_{1}}{L_{2}}=\frac{K_{1}\omega_{2}}{K_{2}\omega_{1}}$
$\frac{L_{1}}{L_{2}}=2\times2=4
L_{1}=\frac{L}{4}$
Was this answer helpful?
0
0
Top Questions on System of Particles & Rotational Motion
- A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$.
Its acceleration at any time $t$ is $x^{-n}$ where $n =$ ____.- JEE Main - 2024
- Physics
- System of Particles & Rotational Motion
- A particle is moving in circular path of radius r speed v such that speed is proportional to radius as \(V∝ r^{\frac{3}{2}}\). Then how does time period of revolution depends on r i.e Trn then \(n\) is.
- JEE Main - 2024
- Physics
- System of Particles & Rotational Motion
- The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is:
- NEET (UG) - 2023
- Physics
- System of Particles & Rotational Motion
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- Physics
- System of Particles & Rotational Motion
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- Physics
- System of Particles & Rotational Motion
View More Questions
Questions Asked in AIEEE exam
- This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. It is not possible to make a sphere of capacity $1$ farad using a conducting material. It is possible for earth as its radius is $6.4 \times 10^6\,m$.
- AIEEE - 2012
- electrostatic potential and capacitance
- A steel wire can sustain $100\, kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
- AIEEE - 2012
- mechanical properties of solids
- The limiting line in Balmer series will have a frequency of (Rydberg constant, $R_{\infty}=3.29\times10^{15}$ cycles/s)
- AIEEE - 2012
- Electromagnetic Spectrum
- Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?
- The ratio of number of oxygen atoms (O) in 16.0 g ozone $(O_3), \,28.0\, g$ carbon monoxide $(CO)$ and $16.0$ oxygen $(O_2)$ is (Atomic mass: $C = 12,0 = 16$ and Avogadro?? constant $N_A = 6.0 x 10^{23}\, mol^{-1}$)
- AIEEE - 2012
- Mole concept and Molar Masses
View More Questions
Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.