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Mass hanging from a cord wound on a wheel or disc: speed or acceleration

This type of question, asked 3 times: 2021 Paper 26, 28 Jun 2022, 28 Jan 2026 S2. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 26

    3
    A cord is wound round the circumference of wheel of radius rr. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mgmg is attached to the cord at the end. The weight falls from rest. After falling through a distance ' hh ', the square of angular velocity of wheel will be:

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  2. Question 2

    28 Jun 2022

    119
    A uniform disc with mass M=4 kgM= 4\text{ }kg and radius R=R = 10 cm10\text{ }cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m=2 kgm= 2\text{ }kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ____\_\_\_\_ N. (Take g=10 ms−2g = 10{\text{ }ms}^{- 2} )

  3. Question 3

    28 Jan 2026 S2

    25
    A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ____\_\_\_\_ J.(g=10 m/s2)J.\left( g = 10\text{ }m/s^{2} \right)