Systems of Particles and Rotational Motion
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Question : 14
Total: 33
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.
Solution:
Mass of hollow cylinder,M = 3 k g
Radius of hollow cylinder,R = 40 c m = 0.4 m
M.I. of the hollow cylinder about its axis
I = M R 2 = 3 k g × ( 0.4 m ) 2 = 0.48 k g m 2
ForceF = 30 N
∴ Torque,τ = F × R = 30 N × 0.4 m = 12 N m
Alsoτ = I α
α =
=
= 25 r a d s − 2
Linear acceleration,a = R α = 0.4 × 25 = 10 m s − 2
Radius of hollow cylinder,
M.I. of the hollow cylinder about its axis
Force
∴ Torque,
Also
Linear acceleration,
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