Question

A horse and a dog are running at the same speed. The mass of the horse is 12 times the mass of the dog. Find out the ratio of their kinetic energies.
A) 1:5
B) 1:12
C) 12:1
D) 1:6

Answer 1

Hint: Kinetic energy is defined as the energy possessed by a body by its motion. It is the energy of motion. Kinetic energy can be transferred between the objects and can be transformed into other kinds of energy.

Complete step by step solution:
We know that kinetic energy is given by the formula, $KE = \dfrac{1}{2}m{v^2}$
Where m is the mass of the object and v is the velocity of the object.
Hence from the above formula, it is clear that the kinetic energy is directly proportional to the mass.
Thus the ratio can be given as $\dfrac{{{{\left( {kinetic{\text{ }}energy} \right)}_{horse}}}}{{{{\left( {kinetic{\text{ }}energy} \right)}_{dog}}}} = \dfrac{{12}}{1}$
$ \Rightarrow \dfrac{{{{\left( {kinetic{\text{ }}energy} \right)}_{horse}}}}{{{{\left( {kinetic{\text{ }}energy} \right)}_{dog}}}} = 12:1$

Hence the correct option is C.

Note:
1. The kinetic energy will be maximum when the potential energy is maximum. This happens when the mass is at the equilibrium position and the velocity is maximum. Kinetic energy depends on the mass of the object and the speed achieved by the object. As the square of the speed is a positive number and also the mass cannot be negative, the kinetic energy of a body cannot be negative.
2. The energy possessed by a body by its position is called potential energy. It depends on the mass of the body and the height up to which the body is lifted.
3. Kinetic energy can also be defined as the work required to accelerate the body for a given mass from its rest state to the stated velocity. Unless the speed changes, the body maintains the same kinetic energy.
4. The basic forms of energy are Electrical, Radiant, Chemical, Mechanical, Nuclear, and Thermal. Many other forms of energy are combinations of these categories.