Question

The mass of the scooter and bike are in the ratio 2:3 but moving with the same speed of 108 km/h. Compute the ratio of their kinetic energy.

Answer 1

Hint: Energy can never be created or destroyed. Energy may be transformed from one form to another. The total energy of a system remains constant in any isolated system of objects. Kinetic energy can be felt when a body is in motion which is equal to $\dfrac{1}{2}mv^2$.

Complete step by step solution:
As given the ratio of mass is 2:3 so,
Let the mass of scooter (m₁) be $2y$
and mass of bike(m₂) be $3y$,
also speed of bike and scooter = 108 km/h = 30 m/s
\[\dfrac{{{\rm{Kinetic \space energy \space of \space scooter\;}}}}{{{\rm{kinetic \space energy \space of \space bike}}}}\] is
$\Rightarrow$ $\dfrac{\dfrac{1}{2}{m_1}v^2}{\dfrac{1}{2}{m_2}v^2}$
$\Rightarrow$ $\dfrac{m_1}{m_2} = \dfrac{2y}{3y}$
$\therefore$ $\dfrac{m_1}{m_2} = \dfrac{2}{3}$

Additional Information:
Energy can be thought of as the property of something that enables it to work. When we say that something has power, we suggest that it is capable of acting and acting on something else. When something happens, energy is added to it. Strength is measured in joules, which are single units. Energy takes different forms. A moving body with a kind of energy motion, Every moving object has the ability to function. By being free to move another object, the moving object can increase one force and cause another object to move its position. While the object moves, it has the ability to function. Energy means the ability to work, so all moving things have energy based on their speed, this type of energy is called kinetic energy. The energy possessed by an object because it is moving is equal to $\dfrac{1}{2}mv^2$.
Many substances contain energy due to their position, potential energy is due to the position or configuration of an object also known as stored energy.
A table has the potential strength of a chest as it can fall to the floor; Sliding from top of the sky, water on the edge of a cataract, cars on top of mountains, something capable of moving forward. The earth has energy under the influence of gravity because it has position; W=mgh=Potential energy

Note: Nearly all mechanical processes consist of interchanges of energy among its kinetic and potential forms and work. When a car drives to the top of a hill, its engine must do work in order to lift the car up. At top the car has an amount of PE equal to the work done in getting it up there. If the engine is turned off, the car can still coast down the hill, and its KE at the bottom of the hiss will be the same as its potential energy at the top - PE -> KE as it goes downhill, KE -> PE as it climbs the second hill.