What is the motion of a body falling freely under gravity?

Option 3 : \(v = \sqrt {2gh} \)

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Concept:

• Under free fall where gravity is the sole influence on the body, the total energy remains the same
• Potential energy gets converted into the kinetic energy
• Potential Energy keeps on decreasing and kinetic energy keeps on increasing
• This is also in confirmation with the law of conservation of energy

Explanation:

From the given condition we know that body is falling freely under the influence of gravity

Hence the equation of velocity can be predicted using any of the two methods given below

By conservation of energy:

• So as explained above if a body is under free fall the energy of the system remains conserved
• i.e., Potential energy = Kinetic energy
  \(mgh = \frac{1}{2}m{v^2}\)
• using this relation, we can find the velocity of the object at any instance

By kinematic equation:

• Similarly, we can use the kinematic equation as well to solve such problems
• Just like in this case as the object starts falling its initial velocity must be zero
  i.e., u = 0
• And as an object falling it will be accelerated due to gravitational force, and its rate of acceleration is given by g
• Thus, the velocity of the object at any instance can be predicted using \({v^2} = {u^2} + 2aS\), here S (displacement) is height so we can assume it as h

∴ \({v^2} = 0 + 2gh \Rightarrow v = \sqrt {2gh} \) 

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