If tension in the string at x=4 h is T1 and T2 at x=h then...

If tension in the string at $x=4 h$ is $T_{1}$ and $T_{2}$ at $x=h$ then $T_{1} / T_{2}$ is (A) 2 (B) 1 (C) $1 / 2$ (D) $1 / 4$Passage 2 A heavy rod of length $\ell$ is released from a height $h$ above the water surface as shown in Fig. $8.45 .$ The rod falls in air and then in water such that it always remains in vertical position. Neglecting the viscous force and drag force on rod while moving in air and water. Also the relative density of the rod is 2 neglecting the loss in energy when rod hitsthe surface. Assuming the water level remains unchanged due to fall of the rod and it touches the bottom of the tank at same speed. The cross-sectional area of the rod is $A$ and is constant. $\rho_{w}=$ density of water

If tension in the string at $x=4 h$ is $T_{1}$ and $T_{2}$ at $x=h$ then $T_{1} / T_{2}$ is
(A) 2
(B) 1
(C) $1 / 2$
(D) $1 / 4$Passage 2 A heavy rod of length $\ell$ is released from a height $h$ above the water surface as shown in Fig. $8.45 .$ The rod falls in air and then in water such that it always remains in vertical position. Neglecting the viscous force and drag force on rod while moving in air and water. Also the relative density of the rod is 2 neglecting the loss in energy when rod hitsthe surface. Assuming the water level remains unchanged due to fall of the rod and it touches the bottom of the tank at same speed. The cross-sectional area of the rod is $A$ and is constant. $\rho_{w}=$ density of water

Key Concepts

Negligible Drag and Viscous Forces

In many idealized physics problems, resistive forces such as drag or viscous friction are assumed to be negligible. This simplification allows the analysis to focus on the primary forces, like gravity and buoyancy, and facilitates the application of conservation laws without the complexities introduced by dissipative forces.

Relative Density

Relative density (or specific gravity) is a measure of how dense a substance is compared to a reference substance, typically water for liquids. It helps in predicting the behavior of an object when immersed in a fluid, as it influences the net buoyant force and the resulting acceleration or motion of the object.

Buoyancy

Buoyancy is the upward force exerted by a fluid on a submerged or partially submerged object, explained by Archimedes' principle. This force is directly related to the volume of fluid displaced by the object and plays a critical role in determining how objects behave when they enter or float in fluids.

Conservation of Energy

This fundamental principle states that in an isolated system, energy can neither be created nor destroyed but only transformed from one form to another. It is extensively used to analyze the motion of bodies, such as falling objects, where gravitational potential energy is converted into kinetic energy, often under idealized conditions that ignore energy losses.

Tension Distribution in a Rope

In a hanging rope or a string under its own weight, the tension varies along its length because each segment must support the weight of the material below it. As a result, the tension is not uniform but changes according to the distance from the free or loaded end, a principle that is important in understanding how forces are distributed in cables and strings.

Static Equilibrium

This concept deals with systems where the net force acting on every part is zero. In problems involving ropes or rods, static equilibrium requires that the forces (such as tension or weight) balance perfectly at every point to maintain a state of rest or constant velocity.

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