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Question #42888

Difficulty: 8/10 | 🟢 Free

The Question

A neutral liquid droplet of mass $M$ is moving with an initial kinetic energy $K_0$ along the positive $x$ -axis in a region of uniform electric field $\vec{E} = E_0 \hat{i}$ . At $x = d$ , it undergoes a perfectly inelastic collision with a stationary dust particle of mass $M$ and charge $+q$ , absorbing it completely. At $x = 2d$ , it undergoes another perfectly inelastic collision with a second identical stationary dust particle of mass $M$ and charge $+q$ , absorbing it as well. What is the kinetic energy of the droplet when it reaches $x = 3d$ ?

Options

A.
$\frac{1}{3} K_0 + \frac{8}{3} q E_0 d$
B.
$\frac{1}{3} K_0 + 3 q E_0 d$
C.
$K_0 + 3 q E_0 d$
D.
$\frac{1}{3} K_0 + \frac{5}{3} q E_0 d$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Quantization of Charge|Conservative Field Path Independence|Variable Mass Systems

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to couple discrete variable mass dynamics with electrostatic potential energy.

A common trap is applying the continuous Work-Energy Theorem ( $\Delta K = \sum W$ ) without accounting for the impulsive, non-conservative nature of the mass accretion process.

Students often correctly calculate the total electrostatic work ( $3qE_0d$ ) but fail to realize that the kinetic energy gained from the electric field between the first and second collisions is partially lost as heat during the second perfectly inelastic collision.

This highlights the critical difference between external work on a system and the internal energy dissipation in open, variable-mass systems.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Quantization of Charge
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free