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Height a rolling body climbs up an incline or curved surface

This type of question, asked 4 times: 2021 Paper 4, 8 Apr 2023, 1 Feb 2024, 5 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    9
    A sphere of radius ' aa ' and mass ' mm ' rolls along horizontal plane with constant speed v0v_{0}. It encounters an inclined plane at angle θ\theta and climbs upward. Assuming that it rolls without slipping how far up the sphere will travel?

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  2. Question 2

    8 Apr 2023

    116
    A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s3\text{ }m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be ___cmcm.
  3. Question 3

    1 Feb 2024

    95
    A disc of radius RR and mass MM is rolling horizontally without slipping with speed vv. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

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  4. Question 4

    5 Apr 2026 S2

    6
    An object of uniform density rolls up the curved path with the initial velocity v0v_{0} as shown in the figure. If the maximum height attained by an object is 7v0210 g\frac{7v_{0}^{2}}{10\text{ }g} (g=g = acceleration due to gravity), the object is a ____\_\_\_\_ .

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