1. Tardigrade
  2. Question
  3. Physics
  4. A cotton reel rolls without sliding such that the point P of the string has velocity v=6 m / s. If r=10 cm and R=20 cm then the velocity of its centre C is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A cotton reel rolls without sliding such that the point $P$ of the string has velocity $v=6 \,m / s$. If $r=10 \,cm$ and $R=20 \,cm$ then the velocity of its centre $C$ isPhysics Question Image

System of Particles and Rotational Motion

Solution:

As cotton reel rolls point of contact of reel with ground will acts as instantaneous axis of rotation.
image
$ v_{P}=\omega(R+r) $
$ \Rightarrow \omega=\frac{v_{p}}{R+r}=20 \,rad/s$
Velocity of centre of reel
$v_{C}=\omega R=\frac{v_{p} R}{(R+r)}=\frac{6 \times 20}{(20+10)}=4 \,m/s$