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Question #42254

Difficulty: 8/10 | 🟢 Free

The Question

Two fixed point masses $M$ and $4M$ are separated by a distance $L$ in an inertial reference frame. A spaceship is moving along the straight line joining the two masses. At a particular instant, the spaceship has an acceleration of magnitude $a = \frac{12GM}{L^2}$ directed towards the mass $4M$ . Inside the spaceship, a small test particle is released. At what instantaneous distance from the mass $M$ (along the line segment joining the masses) should the particle be released so that its initial acceleration relative to the spaceship is zero?

Options

A.
$\frac{L}{2}$
B.
$\frac{L}{3}$
C.
$\frac{2L}{3}$
D.
$\frac{L}{4}$

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

Principle of Superposition|Neutral Equilibrium Points|Frame of Reference Inertial vs Non-Inertial

Why This Question Is Tricky

Common Mistakes

The question tests the student's ability to apply the Principle of Superposition in a non-inertial reference frame.

The common trap is to calculate the static neutral equilibrium point (the L1 Lagrange point) by only equating the gravitational forces, yielding $x = L/3$ .

However, in an accelerating frame, D'Alembert's Principle requires the inclusion of a pseudo force opposite to the frame's acceleration.

This effectively introduces a linear potential term that dynamically shifts the zero-force point.

Students who fail to account for the pseudo force, or apply it in the wrong direction, will arrive at incorrect equilibrium coordinates.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Gravitation - Class 11 Part 1
Concept	Principle of Superposition
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free