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Question #42079

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ and charge $q > 0$ is projected from the origin in the $x-y$ plane with an initial speed $u$ . The $y$ -axis points vertically upwards. A uniform electric field $\vec{E}$ exists in the region such that the equipotential surfaces are vertical planes parallel to the $y-z$ plane, and the electric potential decreases in the positive $x$ -direction. It is given that the magnitude of the electric force on the particle is exactly equal to its weight ( $q|\vec{E}| = mg$ ). The particle is projected at an angle $\theta$ to the positive $x$ -axis. If $\theta$ is chosen such that the particle lands on the $x$ -axis at the maximum possible distance from the origin, what is the ratio of the particle's kinetic energy just before impact to its initial kinetic energy?

Options

A.
$3 + 2\sqrt{2}$
B.
$5$
C.
$2 + 2\sqrt{2}$
D.
$1 + \sqrt{2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Horizontal Range Invariance|Equipotential Surface Geometry|Dipole in Uniform Field|Vector Analysis

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze projectile motion in a non-inertial or coupled force field where standard parabolic symmetry is broken.

The trap lies in blindly applying the standard range formula $R = u^2 \sin 2\theta / g$ and assuming the maximum range occurs at $\theta = 45^\circ$ , which ignores the constant horizontal acceleration provided by the transverse electric field (leading to the incorrect ratio of 5).

By framing the electric field in terms of equipotential surfaces, it also tests the conceptual link between field direction, work done, and effective gravity.

Students must derive the trajectory or range equation from first principles ( $x(t)$ and $y(t)$ with coupled acceleration) and apply the Work-Energy theorem to find the final kinetic energy, avoiding the mistake of calculating work with an incorrect range.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Horizontal Range Invariance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free