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Question:

A proton and an α-particle (with their masses in the ratio of 1:4 and charges in the ratio of 1:2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp:rα of the circular path described by them will be :

1:2

1:3

1:√3

1:√2

Solution:

The correct option is A 1:√2
KE=qΔV
r=√(2mqΔV)/(qB)
r ∝ √(m/q)
rp/rα = √[(mp/qp)/(mα/qα)] = √[(1/1)/(4/2)] = √(1/2) = 1/√2 = 1:√2