Question

Two charged particles P and Q, having the same charge but different masses \( m_p \) and \( m_Q \), start from rest and travel equal distances in a uniform electric field \( \vec{E} \) in time \( t_p \) and \( t_Q \) respectively. Neglecting the effect of gravity, the ratio \( \frac{t_p}{t_Q} \) is:

• A. \( \frac{m_p}{m_Q} \)
• B. \( \frac{m_Q}{m_p} \)
• C. \( \sqrt{\frac{m_p}{m_Q}} \)
• D. \( \sqrt{\frac{m_Q}{m_p}} \)

Hint:

For this problem, remember that the time for a particle to travel a distance depends on the mass and charge, and use the kinematic equations effectively.

Answer 1

The Correct Option is C

The acceleration \( a \) of each particle is given by Newton’s second law: \[ F = ma \quad \text{and} \quad F = qE \quad \Rightarrow \quad a = \frac{qE}{m}. \] Thus, the time taken for each particle to travel the same distance is given by the kinematic equation: \[ d = \frac{1}{2} a t^2 \quad \Rightarrow \quad t = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2dm}{qE}}. \] The ratio of times \( t_p \) and \( t_q \) for particles P and Q is: \[ \frac{t_p}{t_Q} = \sqrt{\frac{m_p}{m_Q}}. \]