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Two different bodies rolling on the same incline: speeds, times, energies or heights compared

This type of question, asked 7 times: 2021 Paper 12, 2021 Paper 13, 25 Jul 2022, 27 Jan 2024, 4 Apr 2024, 24 Jan 2025, 4 Apr 2025. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 12

    17
    A solid cylinder and ring are released from rest in top of inclined plane. Find ratio of their velocities when they reach bottom, assuming pure rolling

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  2. Question 2

    2021 Paper 13

    9
    If a ring and a solid cylinder of same mass and radius are released from the top of an inclined plane. If the time taken by ring to come down is t1t_{1} and time taken by cylinder is t2t_{2} while both perform pure rolling, then choose the correct option.

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  3. Question 3

    25 Jul 2022

    5
    A solid cylinder and a solid sphere, having same mass MM and radius RR, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be:

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  4. Question 4

    27 Jan 2024

    116
    A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7x\frac{7}{x} where xx is ______
  5. Question 5

    4 Apr 2024

    30
    A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed vv. The sphere and the cylinder reaches upto maximum heights h1h_{1} and h2h_{2}, respectively, above the initial level. The ratio h1:h2h_{1}:h_{2} is n10\frac{n}{10}. The value of nn is ____ .
  6. Question 6

    24 Jan 2025

    84
    A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1t_{1} and t2t_{2}, respectively, then

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  7. Question 7

    4 Apr 2025

    21
    A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is x5\sqrt{\frac{x}{5}} where x=x =