CBSE (Science) Class 11CBSE
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# 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. - CBSE (Science) Class 11 - Physics

#### Question

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 the hollow cylinder, m = 3 kg

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

Applied force, F = 30 N

The moment of inertia of the hollow cylinder about its geometric axis:

I = mr2

= 3 × (0.4)2 = 0.48 kg m2

Torque, t = F x r

= 30 × 0.4 = 12 Nm

For angular acceleration alpha, torque is also given by the relation:

t = Ialpha

alpha = t/I = 12/0.48

= 25 " rad s"^(-2)

Linear acceleration = ralpha  = 0.4 xx 25 = 10 ms^(-2)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 7: System of Particles and Rotational Motion
Q: 14 | Page no. 179
Solution 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. Concept: Moment of Inertia.
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