Verified Solution • 2025–26 Session moderate

QJEEM20Ph7b78: JEE Main 2020 Physics - Class 11 JEEM20Ph7b78 Solution: Two uniform circular discs are rotating independently in the…

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg-m2 and 10 rad s–1 respectively while those for the second one are 0.2 kg-m2 and 5 rad s–1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is :

Multiple Choice Options

  • A 203J{{20} \over 3}J
  • B 53J{{5} \over 3}J
  • C 103J{{10} \over 3}J
  • D 23J{{2} \over 3}J

Step-by-Step Verified Solution

Angular momentum conserved for the system

I1 ω1{\omega _1} + I2 ω2{\omega _2} = (I1 + I2) ωf{\omega _f}

⇒\Rightarrow 0.1 × 10 + 0.2 × 5 = (0.1 + 0.2) × ωf{\omega _f}

⇒\Rightarrow ωf{\omega _f} = 203{{20} \over 3}

Kinetic energy of combined disc system

= 12(I1+I2)ωf2{1 \over 2}\left( {{I_1} + {I_2}} \right)\omega _f^2

= 12(0.1+0.2)(203)2{1 \over 2}\left( {0.1 + 0.2} \right){\left( {{{20} \over 3}} \right)^2}

= 203J{{20} \over 3}J

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring