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Chapter 1: Q96PP (page 337)

96. A doubling of the torque produces a greater angular acceleration. Which of the following would do this, assuming that the tension in the rope doesn’t change? (a) Increasing the pulley diameter by a factor of 2; (b) increasing the pulley diameter by a factor of 2; (c) increasing thepulley diameter by a factor of 4; (d) decreasing the pulley diameter by a factor of 2.

Short Answer

Expert verified

Doubling the torque produces a greater angular acceleration where the diameter of the pulley increases by a factor 2. Hence, option b is correct.

Step by step solution

01

Torque and Angular Acceleration

Torque is defined as the product of force and the perpendicular distance between the point of application of force, and the Angular acceleration is the rate of change of velocity at the time.

02

Doubling the torque

The torque of the given system can be written as τ=RTwhere T is the tension force

Given that to assume the tension force as constant then doubling the radius Rdoubles the torque.

Therefore, doubling the torque produces a greater angular acceleration where the diameter of the pulley increases by a factor 2

Hence, option b is correct.

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