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The ratio of periods of α-particle and proton moving on circular path in uniform magnetic field is ______.

Asked in GUJCET 2014 · Circular motion: radius, period and energy

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

Step-by-step solution

Why the other options are wrong

• (2) The reciprocal. T=(2π m)/(qB) is larger for the heavier, lower-charge-per-mass α-particle, so the ratio must exceed 1.
• (3) Uses the mass ratio m_α=4mₚ alone and forgets that the charge is doubled too, q_α=2e. The charge divides the mass factor down to 2.
• (4) Both slips at once — the mass ratio taken upside down and the doubled charge ignored.

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