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Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii R₁ and R₂ respectively. The mass ratio of X and Y is

Asked in JEE Main 29th Jan 2nd Shift 2024 · Circular motion: radius, period and energy

• (1) ((R₁)/(R₂))²
• (2) ((R₂)/(R₁))
• (3) ((R₁)/(R₂))
• (4) ((R₂)/(R₁))²

Step-by-step solution

Why the other options are wrong

• (2) Takes R∝1/m, as if the heavier particle bent more sharply.
• (3) Assumes equal speeds, so r ∝ m, ignoring that equal energy means v ∝ 1/√m.
• (4) Gets m ∝ r² correctly but inverts the ratio.

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