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.
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Options

A. `2.5 m//s`
B. `5 m//s`
C. `4 m//s`
D. `2 m//s`

Answer

C

Explanation

( c) As cotton reel rolls point of contact of reel with ground will acts as instantaneous axis of rotation.
`v_p = omega (R + r)`
`rArr omega= (v_p)/(R + r) = 20 rad//s`
Velocity of centre of reel
`v_C = omega R = (v_p R)/((R + r)) =(6 xx 20)/((20 + 10)) = 4 m//s`.
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