Question

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform mag. field and describe circular path of radius r₁ and r₂ respectively. The ratio of mass of X to that of Y is ___________ 

(a) √(r₁/r₂) 

(b) (r₂/r₁) 

(c) (r₁/r₂)² 

(b) (r₁/r₂)

Answer 1

The correct option  (c) (r₁/r₂)²

Explanation:

Magnetic Force = qVB

centripetal force = (mV²/r)

∴   [(mV²)/r] = qVB

∴   r = (mV/qB)

i.e.   mV = qrB  (1)

also assuming particle starts from rest, final kinetic energy = work done on each particle

∴   (1/2)m₁v₁² = q ∙ V

and  (1/2)m₂v₂² = q ∙ V

∴  m₁V₁² = m₂V₂²   (2)

from (1), m₁V₁ = qBr₁  & m₂V₂ = qBr₂

∴   from (2), m₁[(qBr₁)/m₁]² = m₂ [(qBr₂)/m₂]²

∴   (r₁²/m₁) = (r₂²/m₂) hence (m₁/m₂) = (r₁/r₂)²