A rope is wound around a hollow horizontal cylinder of mass $3 k g$ and radius $40 c m$ . If the rope is pulled with a force of $30 N$ , then the linear acceleration of the rope is

5 m s^{- 2}

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7.5 m s^{- 2}

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10 m s^{- 2}

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12.5 m s^{- 2}

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Solution

The correct option is B $10 m s^{- 2}$
$R = 40 c m$ or $0.4 m$
moment of inertia $I = m r^{2} = 0.48$
Torque about center $F R = I α = 30 \times 0.4 = 0.48 α$
$α = 25 r a d / m^{2}$
linear acceleration $a = α R = 25 \times 0.4 = 10 m s^{- 2}$

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A rope is wound around a hollow horizontal cylinder of mass 3kg and radius 40cm. If the rope is pulled with a force of 30N, then the linear acceleration of the rope is

The correct option is B 10ms−2R=40cm or 0.4mmoment of inertia I=mr2=0.48Torque about center FR=Iα=30×0.4=0.48αα=25 rad/m2linear acceleration a=αR=25×0.4=10 ms−2

A rope is wound around a hollow horizontal cylinder of mass $3 k g$ and radius $40 c m$ . If the rope is pulled with a force of $30 N$ , then the linear acceleration of the rope is

The correct option is B $10 m s^{- 2}$
$R = 40 c m$ or $0.4 m$
moment of inertia $I = m r^{2} = 0.48$
Torque about center $F R = I α = 30 \times 0.4 = 0.48 α$
$α = 25 r a d / m^{2}$
linear acceleration $a = α R = 25 \times 0.4 = 10 m s^{- 2}$