Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Physics
Chapter
Rotational Motion

BITSAT 2021 · Physics · Rotational Motion

A round disc of moment of inertia I_ 2 about its axis perpendicular...

A round disc of moment of inertia I2\mathrm{I}_{2} about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I1\mathrm{I}_{1} rotating with an angular velocity ω\omega about the same axis. The final angular velocity of the combination of discs is

Options

  1. A\frac{\left(\mathrm{I}1+_{1}+\mathrm{I}_{2}\right) \omega}{\mathrm{I}_{1}}
  2. B\frac{\mathrm{I}_{2} \omega}{\mathrm{I}1+_{1}+\mathrm{I}_{2}}
  3. Cω\omega
  4. D\frac{\mathrm{I}_{1} \omega}{\mathrm{I}1+_{1}+\mathrm{I}_{2}}

Correct answer

D. \frac{\mathrm{I}_{1} \omega}{\mathrm{I}1+_{1}+\mathrm{I}_{2}}

Step-by-step solution

Total angular momentum of the system initially Li=\mathrm{L}_{\mathrm{i}}=\mathrm{I}1w+_{1} \mathrm{w}+\mathrm{I}2(0)=_{2}(0)=\mathrm{I}1w)Totalangularmomentum_{1} \mathrm{w}) Total angular momentum of thesystemfinally(Lf=(I1+I2)w2)Accordingtoconservationofangularmomentumi.e.(Li=Lf)the system finally (L_{f}=\left(I_{1}+I_{2}\right) w_{2}) According to conservation of angular momentum i.e. (\mathrm{L}_{\mathrm{i}}=\mathrm{L}_{\mathrm{f}})⇒I1ω=(I1+I2)ω2⇒ω2=I1ωI1+I2\begin{aligned}&\Rightarrow \mathrm{I}_{1} \omega=\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right) \omega_{2}\\ &\Rightarrow \omega_{2}=\frac{\mathrm{I}_{1} \omega}{\mathrm{I}_{1}+\mathrm{I}_{2}} \end{aligned}$$
Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

The moment of inertia of a cube of mass m and side a about one of its edges is equal to BITSAT 2024The torque of a force 5 i +3 j -7 k about the origin is τ . If the force acts on a… BITSAT 2023A disc is rolling without slipping on a surface. The radius of the disc is R . At t=0… BITSAT 2023Four holes of radius 5 cm are cut from a thin square plate of 20 cm and mass 1 kg . The… BITSAT 2022A solid sphere of 80 kg and radius 15 m moving in a space becomes a circular disc of… BITSAT 2022Three particles, each of mass m gram, are situated at the vertices of an equilateral… BITSAT 2021A solid cylinder and a hollow cylinder both of the same mass and same external diameter… BITSAT 2020M.I of a circular loop of radius R about the axis in figure is BITSAT 2020 Full Rotational Motion list All BITSAT PYQs