Rotational Motion

JEE Main level, single correct, medium

210 of 280

Question 210 of 280

Two discs have moments of intertia I1{I}_{1} and I2{I}_{2} about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1{\omega }_{1} and ω2{\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:

Show answer and solution

Answer: (C) I1I22(I1+I2)(ω1−ω2)2\dfrac{{I}_{1}{I}_{2}}{2\left({I}_{1}+{I}_{2}\right)}{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}

Angular momentum conservation
I1ω1+I2ω2=(I1+I2)ω{I}_{1}{\omega }_{1}+{I}_{2}{\omega }_{2}=\left({I}_{1}+{I}_{2}\right)\omega
ω=I1ω1+I2ω2I1+I2\omega =\dfrac{{I}_{1}{\omega }_{1}+{I}_{2}{\omega }_{2}}{{I}_{1}+{I}_{2}}
Loss =12I1ω12+12I2ω22−12(I1+I2)ω2=\dfrac{1}{2}{I}_{1}{\omega }_{1}^{2}+\dfrac{1}{2}{I}_{2}{\omega }_{2}^{2}-\dfrac{1}{2}\left({I}_{1}+{I}_{2}\right){\omega }^{2}
=12I1ω12+12I2ω22−12(I1+I2)(I1ω1+I2ω2I1+I2)2=\dfrac{1}{2}{I}_{1}{\omega }_{1}^{2}+\dfrac{1}{2}{I}_{2}{\omega }_{2}^{2}-\dfrac{1}{2}\left({I}_{1}+{I}_{2}\right){\left(\dfrac{{I}_{1}{\omega }_{1}+{I}_{2}{\omega }_{2}}{{I}_{1}+{I}_{2}}\right)}^{2}
=12I1I2(I1+I2)(ω1−ω2)2=\dfrac{1}{2}\dfrac{{I}_{1}{I}_{2}}{\left({I}_{1}+{I}_{2}\right)}{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}
Ei−Ef=I1I2(ω1−ω2)22(I1+I2){E}_{i}-{E}_{f}=\dfrac{{I}_{1}{I}_{2}{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}}{2\left({I}_{1}+{I}_{2}\right)}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Rotational dynamics and rolling simulationDrag the sliders and watch the numbers in this question change.Revise Rotational Motion firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Rotational Motion (Angular momentum and Angular impulse), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.