Question

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ respectively. The ratio of masses of X and Y is

• A. \( \left(\dfrac{R_1}{R_2}\right)^{1/2} \)
• B. \( \left(\dfrac{R_2}{R_1}\right)^{1/2} \)
• C. \( \left(\dfrac{R_1}{R_2}\right)^2 \)
• D. ((R₂)/(R₁))²

Hint:

Magnetic radius after acceleration depends on square root of mass.

Answer 1

The Correct Option is C

Step 1: From acceleration through potential V: (1)/(2)mv² = qV ⟹ v = √((2qV)/(m))
Step 2: Radius in magnetic field: R = (mv)/(qB) ⟹ R ∝ √(m)
Step 3: Hence, (mX)/(mY) = ((R₁)/(R₂))²