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A proton and a deutron (q = +e, m = 2.0 u) having same kinetic energies enter a region of uniform magnetic field B⃗, moving perpendicular to B⃗. The ratio of the radius r_d of deutron path to the radius rₚ of the proton path is

Asked in JEE Main 9th April 2nd Shift 2024 · Circular motion: radius, period and energy

• (1) 1:2
• (2) 1:√2
• (3) 1:1
• (4) √2:1

Step-by-step solution

Why the other options are wrong

• (1) Uses r ∝ 1/m and also inverts the ratio.
• (2) Inverts the ratio (rₚ : r_d instead of r_d : rₚ).
• (3) Assumes equal kinetic energy means equal momentum.

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