What is the answer for this weird question?

Before I start writing my solution, I need to give you some information regarding this problem.

Theory Of Relativity:

Albert Einstein gave many laws of motion in his theory of relativity. We are going to discuss only one particular law i.e. $E = mc^{2}$ .

Actually this is wrong... Well, I mean the way of writing the equation is wrong. Albert Einstein actually did not give that $E= mc^{2}$ . He wrote in his paper that $m = \dfrac{E}{c^{2}}$ . What does this actually mean? Suppose there is a boy whose mass is $25 kg$ when weighed. What is his mass when he is moving with a velocity say $25 m/s$ ? We will make it somewhat clear by giving another example.

Actually when we switch on a flashlight, the chemical energy in the battery is converted into light energy. So, the chemical inside the battery decreases. I mean it's mass gradually reduces. Where this mass going to? This mass actually converted into light energy(Indirectly). So, what actually Einstein's Theory of Relativity says is that

$m_{total} = m_{actual} +m_{extra}$

where $m_{actual}$ is the actual mass. What is this $m_{extra}$ ? This extra is what Einstein is suggesting. It is the mass due to the energy possessed by it. But this $m_{extra}$ is very very very small as compared $m_{actual}$ . So, it is neglected in Newtonian Mechanics. But it becomes comparable value in case of high velocity moving objects like light. It is given by $m_{extra} = \dfrac{E}{c^2}$ , where $E$ is the energy of the body and $c$ is the speed of light.

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So, How is this going to be helpful for us?

Actually, as the masses are different, the potential energy of the systems in different cases is different. But, the actual total mass is same. It can be calculated that potential energies of the systems in situation $A$ and $B$ are calculated to be $3000 J$ and $5000 J$ respectively (from given data). We have to calculate

$m_{2} - m_{1} = m_{actual_{2}} + m_{extra_{2}} - m_{actual_{1}} - m_{extra_{1}}$

where $m_{actual_{j}}$ and $m_{extra_{j}}$ denotes the actual and extra mass in situation $j$ , where $j={1,2}$ .

But, $m_{actual_{1}} = m_{actual_{i}} = 400 kg$ So,

$m_{2} - m_{1} = m_{extra_{2}} - m_{extra_{1}}$

As I had said before $m_{extra} = \dfrac{E}{c^2}$ . But since we have got the energy of combined mass in situation $1$ is equal to $3000 J$ . So, we get $m_{extra_{1}} = \dfrac{3000}{c^2}$ and similarly $m_{extra_{2}} = \dfrac{5000}{c^2}$ .

So, $m_{2} - m_{1} = m_{extra_{2}} - m_{extra_{1}} = \dfrac{2000}{c^2}$ .

Therefore, $\lfloor 10^{15} \times (m_{2} - m_{1}) \rfloor = \lfloor 10^{15} \times \dfrac{2000}{c^2} \rfloor = \boxed{22}$ .

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Note: Speed of light = $299792458 m/s$ .

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