Question

Show that the quantity $\dfrac{{2K}}{{{v^2}}}$ has the unit of mass, where $K$ is the kinetic energy of the body.

Answer 1

Hint:-In this question, we can deduce the formula of kinetic energy in a way that the whole formula changes into the formula of mass. It can be done by changing the places of the quantities according to the mathematical operations.

Complete step-by-step solution:
We know that if \[m\] is the mass of the body and \[v\] is the velocity of the body then the kinetic energy \[K\] of the body is given as
$K = \dfrac{1}{2}m{v^2}$
Now, we can write above equation as given below-
$M = \dfrac{{2K}}{{{v^2}}}$
Thus $\dfrac{{2K}}{{{v^2}}}$is equal to the mass of the body.
Hence, $\dfrac{{2K}}{{{v^2}}}$has the unit of mass.

Additional Information: - Kinetic energy is the of an object is the energy that a moving object possesses. It is work done which is needed to accelerate a body from rest to a velocity. It is also known as movement energy. It can be transformed into and from different types of energy.
For example, a cyclist accelerates a bicycle by using chemical energy which he got from the food. This chemical energy is converted into kinetic energy.
Similarly, a spacecraft launches and gains considerable kinetic energy by using chemical energy which it got from the fuel and reached the required orbital velocity.

Note:- In this question, we have to remember the formula of kinetic energy to solve this question. We have to keep in mind that while changing the places of quantities, the mathematical operations such as cross product are followed properly. If the left side and right side are equal to each other then both sides have the same unit.