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Ratio of radii of particles with equal momentum or speed in a field

This type of question, asked 4 times: 2021 Paper 3, 2021 Paper 15, 26 Jun 2022, 3 Apr 2025. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 3

    9
    A proton, a deuteron and an α\alpha particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is ____\_\_\_\_ and their speeds are in the ratio ____\_\_\_\_.

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  2. Question 2

    2021 Paper 15

    16
    Two particles having identical masses and charges 2Q and Q are moving with velocities VV and 2 V2\text{ }V respectively, In uniform magnetic field BB. Find ratio of the radius of circle describe by them

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  3. Question 3

    2021 Paper 15

    13
    Two charges of equal magnitude are thrown with speeds ratio (3:2)(3:2) perpendicular to the magnetic field. If their masses are in the ratio of 1:21:2. Find ratio of the radii?

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  4. Question 4

    26 Jun 2022

    14
    A proton and an alpha particle of the same speed enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is:

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  5. Question 5

    3 Apr 2025

    95
    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If oxygen ion (O−2)\left( O^{- 2} \right) and Hydrogen ion (H+)\left( H^{+} \right)enter normal to the magnetic field with equal momentum, then the path of O−2O^{- 2} ion has a smaller curvature than that of H+H^{+}. Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statement, choose the correct answer from the options given below

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