Ncert Exercises & Solutions

Question 7. 14. A rope of negligible mass is wound around 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.

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,

τ = F \times r

= 30 × 0.4 = 12 Nm
For angular acceleration

α

, torque is also given by the relation:

τ = 1 α α = \frac{τ}{I} = \frac{12}{0.48} = 25 rad s^{- 2}

Linear acceleration

= rα = 0.4 \times 25 = 10 m s^{- 2}

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions