Three weights W, 2W and 3W are connected to identical springs suspended form rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that

The correct answer is: All will be at the same distance.

To understand why, we need to think carefully about what happens to a spring-mass system during free fall.

Step 1: Normal situation (before free fall)

When the system is at rest (or in normal equilibrium hanging from the rod), each spring stretches by a different amount to support the weight attached to it. For a spring with spring constant k, the extension x caused by a weight W is given by Hooke's Law:

kx=W\Rightarrow x=\frac{W}{k}

So normally, the spring holding 3W stretches the most, and the spring holding W stretches the least. The positions of the weights from the rod would all be different.

Step 2: What happens during free fall?

When the entire assembly (rod + springs + weights) is released into free fall, every part of the system — the rod, the springs, and all the weights — accelerates downward with exactly the same acceleration, which is g (acceleration due to gravity).

Inside a freely falling frame, the effective gravitational field is zero. This is the principle of equivalence — free fall is equivalent to being in a zero-gravity (weightless) environment.

Step 3: Forces on each weight during free fall

Consider any weight (say, of mass m) attached to a spring during free fall. The forces on it are:

→ Gravitational force (downward): mg
→ Spring restoring force (upward): F=kx

Applying Newton's second law (taking downward as positive), since the weight also accelerates at g:

mg-kx=ma=mg

Simplifying:

-kx=0\Rightarrow x=0

This means the net extension in every spring becomes zero during free fall!

Step 4: What does x = 0 mean for each spring?

If every spring has zero extension, then no spring is stretched — each weight hangs at the natural (unstretched) length of the spring below the rod. Since all three springs are identical (same natural length), all three weights — W, 2W, and 3W — will be at the same distance from the rod.

The mass of the weight attached to the spring is completely irrelevant here, because in free fall, effective weight (apparent weight) of every object becomes zero. There is no force to stretch any of the springs, regardless of how heavy the weight is.

Conclusion:

During free fall, the effective weight of each body becomes zero. Since no weight acts on any spring, none of the identical springs stretch. All three weights — W, 2W, and 3W — are therefore positioned at the natural length of their respective springs from the rod, meaning all three are at the same distance from the rod.