Given below are two statements: one is labelled as A s s e r t i o n A and the other is labelled as Reason R
Assertion A : If Oxygen ion (O⁻²) and Hydrogen ion (H⁺)enter normal to the magnetic field with equal momentum, then the path of O⁻² ion has a smaller curvature than that of 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 statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

With equal momentum, only the charge sets the radius: r = p/qB, and mass drops out entirely.

1. Radius from momentum. For a charge moving perpendicular to B, the magnetic force provides the centripetal force: qvB = mv²/r. Since mv = p, the mass is hidden inside p.

   r = mv/qB = p/qB

2. Check Assertion A. With equal p and the same B, r ∝ 1/q. O²⁻ carries 2e and H⁺ carries e, so r_O = 1/2 r_H. The assertion's "smaller curvature" means a smaller radius of curvature, and that is true. The opposite signs only make the two ions bend in opposite directions.
3. Check Reason R. A proton and an electron have the same charge magnitude e. With the same momentum, r = p/eB is the same for both. The proton's larger mass does not matter here, so R is false.
4. So. A is true and R is false, which is option (c).

The idea to keep. When momentum is fixed, r = p/qB depends only on charge. Mass matters only when speed or kinetic energy is fixed, so always check which quantity the question keeps equal.

Answer from the NTA final answer key. Solution by PrepWiser.