7.14 A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.

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Vishal Baghel | Contributor-Level 10

4 months ago

Mass of the hollow cylinder, m = 3 kg

Radius of the hollow cylinder, r = 40 cm = 0.4 m

Applied force, F = 30 N

The MI of the hollow cylinder about its axis,

I = $ω^{2}$ = 3 x 0.4 x 0.4 = 0.48 kgm²

Torque, $ω_{2}^{2}$ = 30 x 0.4 = 12 Nm

For angular acceleration $ω_{1}^{2}$ , torque is given by

$m r^{2}$ = I x $τ = F x r$ or

$α$ / I = 12 / 0.48 = 25 rad/s

Linear acceleration = r x $τ$ = 0.4 x 25 = 10 m/s²

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