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Question #42939

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ and charge $q$ is constrained to move along a smooth quarter-circular track of radius $R$ in the $xy$ -plane, from point $A(R, 0)$ to point $B(0, R)$ . The region contains a viscous fluid that exerts a drag force on the particle given by $\vec{F}_d = -\frac{m}{2R} v^2 \hat{v}$ , where $v$ is the instantaneous speed and $\hat{v}$ is the unit vector in the direction of velocity. A uniform electrostatic field $\vec{E} = E_0 \hat{j}$ exists in the region. If the particle is projected from point $A$ with an initial kinetic energy $K_0$ , what is its kinetic energy upon reaching point $B$ ? (Assume gravity is negligible).

Options

A.
$K_0 e^{-\pi/2} + \frac{q E_0 R}{2} \left( 1 - e^{-\pi/2} \right)$
B.
$K_0 + q E_0 R$
C.
$K_0 \left( 1 - \frac{\pi}{2} \right) + q E_0 R$
D.
$K_0 e^{\pi/2} + \frac{q E_0 R}{2} \left( 1 + e^{\pi/2} \right)$

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

Conservative Field Path Independence|Work-Energy Theorem Validity|Conservative Force Field

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem in the presence of both conservative and non-conservative, path-dependent forces.

A common trap for students is to blindly apply the conservation of mechanical energy ( $\Delta K + \Delta U = 0$ ) because they see an electrostatic field, completely ignoring the non-conservative drag force (Option B).

Even if they recognize the drag force, they might incorrectly assume it does constant work or fail to set up the differential equation linking kinetic energy to the path variable $\theta$ .

By making the drag force proportional to $v^2$ , the work done by drag becomes directly proportional to the instantaneous kinetic energy, forcing the student to abandon simple algebraic shortcuts and solve a first-order linear differential equation to find the final kinetic energy.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Conservative Field Path Independence
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free