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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.
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$ v_{P}=\omega(R+r) $
$ \Rightarrow \omega=\frac{v_{p}}{R+r}=20 \,rad/s$
Velocity of centre of reel
$v_{C}=\omega R=\frac{v_{p} R}{(R+r)}=\frac{6 \times 20}{(20+10)}=4 \,m/s$