A block of mass m is attached by means of a spring to the...

A block of mass $m$ is attached by means of a spring to the bottom of a tank of water as shown in Fig. $8.43$. At equilibrium, the spring is under compression. If the tank is now allowed to fall freely, then choose the correct alternative(s). (A) The spring comes to its relaxed position. (B) The spring compresses more than its equilibrium compression. (C) The buoyant force becomes zero. (D) There will be some elongation is the spring.

A block of mass $m$ is attached by means of a spring to the bottom of a tank of water as shown in Fig. $8.43$. At equilibrium, the spring is under compression. If the tank is now allowed to fall freely, then choose the correct alternative(s).
(A) The spring comes to its relaxed position.
(B) The spring compresses more than its equilibrium compression.
(C) The buoyant force becomes zero.
(D) There will be some elongation is the spring.

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Key Concepts

Spring Equilibrium

A spring reaches equilibrium when its restoring force balances the other forces acting on it. In a stationary situation, additional forces such as gravity and buoyancy may cause the spring to be either compressed or extended. However, once the system enters a state of free fall and experiences weightlessness, these forces vanish, allowing the spring to relax to its natural, uncompressed position.

Weightlessness in Free Fall

When an entire system is in free fall, every object within it experiences the same acceleration, resulting in an effective weightlessness. This means that relative to the falling system, the forces due to gravity cancel out, and objects behave as though they are in a zero-gravity environment, affecting how forces are balanced within the system.

Buoyant Force

Buoyant force arises from a pressure gradient in a fluid, which is normally caused by gravity. In a free-fall environment, the fluid is in a state of weightlessness because all parts of it accelerate uniformly, eliminating the pressure gradient. This results in the buoyant force essentially disappearing within the free-falling system.

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