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

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 (A) 2.5 m/s (B) 5 m/s (C) 4 m/s (D) 2 m/s

Tardigrade Admin · Accepted Answer

As cotton reel rolls point of contact of reel with ground will acts as instantaneous axis of rotation.

v_{P} = ω (R + r)

\Rightarrow ω = \frac{v _{p}}{R + r} = 20 r a d / s

Velocity of centre of reel

v_{C} = ω R = \frac{v _{p} R}{( R + r )} = \frac{6 \times 20}{( 20 + 10 )} = 4 m / s

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

2.5 m/s

5 m/s

4 m/s

2 m/s

As cotton reel rolls point of contact of reel with ground will acts as instantaneous axis of rotation. vP​=ω(R+r) ⇒ω=R+rvp​​=20rad/s Velocity of centre of reel vC​=ωR=(R+r)vp​R​=(20+10)6×20​=4m/s

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

As cotton reel rolls point of contact of reel with ground will acts as instantaneous axis of rotation.

$v_{P} = ω (R + r)$
$\Rightarrow ω = \frac{v _{p}}{R + r} = 20 r a d / s$
Velocity of centre of reel
$v_{C} = ω R = \frac{v _{p} R}{( R + r )} = \frac{6 \times 20}{( 20 + 10 )} = 4 m / s$