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A proton and a α-particle are placed in uniform electric field. Accelerations produced in them are aₚ and a_α respectively. Then aₚ : a_α will be ________.

Asked in GUJCET 2026 · Deflection and projectile motion

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

Step-by-step solution

Why the other options are wrong

• (1) The correct ratio written the wrong way round: 1 : 2 is a_α : aₚ, not aₚ : a_α. The proton has the larger charge-to-mass ratio, so it is the proton that accelerates more, and its number belongs first.
• (3) Uses the masses alone, m_α : mₚ = 4 : 1, as if the two particles felt the same force. The α-particle carries charge 2e, so the force on it is twice that on the proton, which cancels half of the mass disadvantage.
• (4) Reads the mass ratio mₚ : m_α = 1 : 4 straight off as the acceleration ratio, as though a grew with mass. In a given field a=(qE)/m, so a falls as m rises and also depends on q.

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