Question

An object of mass $'m'$ and velocity $'v'$ has kinetic energy $200J$. Find the new kinetic energy if the mass of the object becomes double and velocity is still the same.

Answer 1

Hint: From the information given in the question, all the values of the variables have to be deduced and substituted in the formula of kinetic energy. Now, the value of the mass should be changed as referred to in the question and the value of the new kinetic energy can be found. Thereafter the values of both the kinetic energies have to be Compared to get the answer.

Formula Used:
$K.E. = \dfrac{1}{2}m{v^2}$
Where $K.E.$ is the kinetic energy.
$m$ is the mass of the object.
$v$ is the velocity of the object.

Complete step by step answer:
Let us consider the mass of the object be $'m'$ and the velocity be $'v'$. The kinetic energyi.e. ${(K.E.)_1}$for the given arrangement is given as $200J$. Mathematically, we can write it as,
${(K.E.)_1} = \dfrac{1}{2}m{v^2}$
$ \Rightarrow 200J = \dfrac{1}{2}m{v^2}$
$ \Rightarrow m{v^2} = 400J......(1)$
Now, the mass of the object has been doubled. Therefore, the new value of the mass is $'2m'$ while the value of velocity remains the same, i.e. $'v'$. Let the new kinetic energy is ${(K.E.)_2}$ .We now have to substitute the values in the formula of kinetic energy to get,
${(K.E.)_2} = \dfrac{1}{2} \times (2m) \times {v^2}$
${(K.E.)_2} = m{v^2}......(2)$
On comparing and substituting the values of equation (1) in equation (2), we get,
${(K.E.)_2} = 400J$
Therefore, the new kinetic energy is $400J$.

Note:
We all know the fact that energy can neither be created nor be destroyed. It can only be transformed from one form to the other. When work is done on an object, energy gets transferred and the object starts to move. This energy which is due to the virtue of motion of the object is known as kinetic energy. It is a scalar quantity i.e. only the magnitude is required to describe it. From the formula, we can infer that the kinetic energy is directly proportional to the mass of the object. So, if the mass is doubled and velocity is constant, automatically the value of the kinetic energy will get doubled.