Question

A body is dropped from a certain height. When it lost an amount of potential energy, ‘U’ it subsequently had a velocity ‘v’. The mass of the body is

$$A. \dfrac{{2U}}{{{v^2}}} \\\ B. \dfrac{U}{{2{v^2}}} \\\ C. \dfrac{{2U}}{v} \\\ D. \dfrac{{2{U^2}}}{{{v^2}}} \\\$$

Answer 1

According to the law of conservation of energy, energy can neither be created nor be destroyed. It can only transform from one form into another form. Thus using the law, we will compare the loss of potential which is actually converted into the gain of kinetic energy and putting mass, the subject of the equation.

Complete step by step answer:
Energy of a body is the ability of the body to do work. Energy can exist in different types such as potential, kinetic, thermal, electrical, chemical and nuclear and many other various forms.
The law of conservation of energy is written as follow; “In a closed system, that is, a system that is isolated from its surroundings, the total energy of the system is conserved.” In simple words, energy can neither be created nor destroyed; it can only be converted from one form to another. Here, U is the potential energy which is transferred into kinetic energy. The kinetic energy is given as
$K = \dfrac{1}{2}m{v^2}$
Where $m$ is the mass and $v$ is the velocity of the body, while $K$ is the kinetic energy.
Now, as the potential energy is transferred into kinetic energy, the amount of lost potential energy I equate to the gain of the kinetic energy.
Thus, we have

$$K = U \\\ \Rightarrow \dfrac{1}{2}m{v^2} = U \\\ \therefore m = \dfrac{{2U}}{{{v^2}}} \\\$$

Thus option A is the correct answer.

Note: Here, we assume that the resistance/ friction due to air is negligible and hence ignore it. Also, we assume that no other force is applied on the body and the body only gets transformed from potential energy into the kinetic energy. Here, we take potential energy as U, but this energy depends on height as follows: U=mgh.