JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2021
- Hard
- MCQ
Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\frac{{I}_{1} {I}_{2}}{2\left({I}_{1}+{I}_{2}\right)}\left(\omega_{1}-\omega_{2}\right)^{2}\)
Step-by-step Solution
Detailed explanation
From conservation of angular momentum we get
\({I}_{1} \omega_{1}+{I}_{2} \omega_{2}=\left({I}_{1}+{I}_{2}\right) \omega\)
\(\omega=\frac{{I}_{1} \omega_{1}+{I}_{2} \omega_{2}}{{I}_{1}+{I}_{2}}\)
\({k}_{{i}}=\frac{1}{2} {I}_{1} \omega_{1}^{2}+\frac{1}{2} {I}_{2} \omega_{2}^{2}\)
\({k}_{{f}}=\frac{1}{2}\left({I}_{1}+{I}_{2}\right) \omega^{2}\)
\({k}_{{i}}-{k}_{{f}}=\frac{1}{2}\left[{I}_{1} \omega_{1}^{2}+{I}_{2} \omega_{2}^{2}-\frac{\left({I}_{1} \omega_{1}+{I}_{2} \omega_{2}\right)^{2}}{{I}_{1}+{I}_{2}}\right]\)
Solving above we get
\({k}_{{i}}-{k}_{{f}}=\frac{1}{2}\left(\frac{{I}_{1} {I}_{2}}{{I}_{1}+{I}_{2}}\right)\left(\omega_{1}-\omega_{2}\right)^{2}\)
More questions from Physics
- A circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is
JEE Mains 2017 Hard - The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given byJEE Mains 2023 Medium
- The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :
JEE Mains 2025 Hard - A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \(\frac{7}{\mathrm{x}}\) where \(\mathrm{x}\) is___________.JEE Mains 2024 Hard
- A plane electromagnetic wave of frequency \(35\ \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\ \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______.JEE Mains 2024 Hard
- The gap between the plates of a parallel plate capacitor of area \(A\) and distance between plates \(d\), is filled with a dielectric whose permittivity varies linearly from \({ \varepsilon _1}\) at one plate to \({ \varepsilon _2}\) at the other. The capacitance of capacitor isJEE Mains 2014 Hard
More PYQs from JEE Mains
- Two charges each of magnitude \(0.01\,C\) and separated by a distance of \(0.4\,mm\) constitute an electric dipole. If the dipole is placed in an uniform electric field ' \(\vec{E}\) ' of \(10\,dyne/C\) making \(30^{\circ}\) angle with \(\overrightarrow{ E }\), the magnitude of torque acting on dipole is :JEE Mains 2023 Easy
- A light ray is incident on a glass slab of thickness \(4 \sqrt{3} \mathrm{~cm}\) and refractive index \(\sqrt{2}\). The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _______ \(\mathrm{cm}\). \(\left(\right.\) Given \(\left.\sin 15^{\circ}=0.25\right)\)JEE Mains 2024 Hard
- For the forward biased diode characteristics shown in the figure, the dynamic resistance at \({I}_{{D}}=3 \,{mA}\) will be \(.....\,\Omega\)
JEE Mains 2021 Medium - Refer to the circuit diagram given below. The heat generated across the \(6\,\Omega\) resistance in \(100\) second is \(\dfrac{\alpha}{100}\) J. The value of \(\alpha\) is _______. (Nearest integer)
JEE Mains 2026 Hard - Two cylindrical vessels of equal cross sectional area of \(2 \mathrm{~m}^2\) contain water up to height 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is \(10^3 \mathrm{~kg} / \mathrm{m}^3\) and \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))JEE Mains 2025 Medium