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A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm and then the entire arrangement is placed on a smooth horizontal surface. What is the angular acceleration (in ) of the cylinder if the rope is pulled with a force of 30 N?
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The correct answer is:
10
Given, M = 3 kg
R = 40 cm = 0.40 m
F = 30 N
Moment of inertia of the hollow cylinder about its axis of symmetry
I = MR2
= 3 × (0.40)2 = 0.48 kg-m2
Torque acting on the cylinder by the applied force,
= F × R
= 30 × 0.40 = 12 N-m.
Angular acceleration produced in cylinder,
Linear acceleration, a = R
= 0.40 × 25 = 10.0 m/s2
R = 40 cm = 0.40 m
F = 30 N
Moment of inertia of the hollow cylinder about its axis of symmetry
I = MR2
= 3 × (0.40)2 = 0.48 kg-m2
Torque acting on the cylinder by the applied force,
= F × R
= 30 × 0.40 = 12 N-m.
Angular acceleration produced in cylinder,
Linear acceleration, a = R
= 0.40 × 25 = 10.0 m/s2
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