Two bodies of masses m1 and m2 are dropped from heights H and 2 H respectively. The ratio of tim

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Two bodies of masses m1 and m2 are dropped from heights H...

Two bodies of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ are dropped from heights $\mathrm{H}$ and $2 \mathrm{H}$ respectively. The ratio of time taken by the bodies to touch the ground is ...
(A) $(1 / 2)$
(B) 2
(C) $(1 / \sqrt{2})$
(D) $(\sqrt{2} / 1)$

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Key Concepts

Kinematic Equations and Square Root Relationship

The kinematic equation for displacement in uniformly accelerated motion, s = 1/2 g t^2, illustrates that the time taken to fall a certain height is proportional to the square root of that height. Thus, if two objects are dropped from different heights, the ratio of their fall times can be found by taking the square root of the ratio of the heights, demonstrating that doubling the height increases the fall time by a factor of ?2.

Uniform Acceleration in Free Fall

In free fall, an object accelerates uniformly under the influence of gravity, meaning that its acceleration remains constant throughout the motion. This principle allows the use of kinematic equations to analyze the motion of objects dropped from any height, regardless of their mass, as gravity provides a constant acceleration to all objects near Earth’s surface in the absence of air resistance.

Mass Independence in Gravitational Fields

When objects are in free fall, the acceleration due to gravity is independent of their mass. This means that all objects, irrespective of their mass, will fall at the same rate under gravity. This principle is essential in understanding that the time taken to fall is determined solely by the height from which an object is dropped, not by its mass.

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