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String wound on a wheel pulled by a force: angular acceleration or speed

This type of question, asked 3 times: 13 Apr 2023, 9 Apr 2024, 2 Apr 2025. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    13 Apr 2023

    117
    A light rope is wound around a hollow cylinder of mass 5 kg5\text{ }kg and radius 70 cm70\text{ }cm. The rope is pulled with a force of 52.5 N52.5\text{ }N. The angular acceleration of the cylinder will be___ rad s−2{rad\text{ }s}^{- 2}.

  2. Question 2

    9 Apr 2024

    25
    A string is wrapped around the rim of a wheel of moment of inertia 0.40kgm20.40kgm^{2} and radius 10 cm10\text{ }cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N40\text{ }N. The angular velocity of the wheel after 10 ss is xrad/sxrad/s, where xx is ______

  3. Question 3

    2 Apr 2025

    96
    A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of 2rad/s22rad/s^{2}. Moment of inertia of the wheel is ____\_\_\_\_ kgm2kgm^{2}. (Acceleration due to gravity =10 m/s2= 10\text{ }m/s^{2} )

  4. Question 4

    2 Apr 2025

    3
    A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :

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