Question

If the speed of light were 50% of the present value, by what % the energy released will it decrease?
A. \[100\% \]
B. \[50\% \]
C. \[25\% \]
D. \[75\% \]

Answer 1

Hint: The above problem can be resolved by using Einstein's energy relation. In this relation, the energy is correlated with the velocity of light. And as the final speed of light is 50% of the initial speed, therefore the equations can be solved by taking the ratio of the energies at initial and at final.

Complete step by step answer:
Let E be the initial value of energy released and c be the initial speed of light. As the speed of light is 50%, then the final speed of light is given as,
\[{c_2} = \dfrac{{50}}{{100}}c.............\left( 1 \right)\]
 Using the Einstein’s energy relation for the initial and final condition as,
\[\begin{array}{l}
E = m{c^2}....................\left( 2 \right)\\
{E_2} = mc_2^2......................\left( 3 \right)
\end{array}\]
Taking the ratio of equation 3 and 2 as,
\[\begin{array}{l}
\dfrac{{{E_2}}}{E} = \dfrac{{m \times {{\left( {\dfrac{{50}}{{100}}c} \right)}^2}}}{{m{c^2}}}\\
\dfrac{{{E_2}}}{E} = \dfrac{1}{4}\\
{E_2} = \dfrac{{25}}{{100}}E
\end{array}\]
The above result shows that the energy will decrease by 25 % .
Therefore, the energy released will be decreased by 25%

So, the correct answer is “Option C”.

Note:
To solve the given problem, one must be clear with the concept of Einstein's energy equation. According to this equation, the universe is the only comprise of the mass and the energy. Both the mass and the energy can never be destroyed; rather, one is convertible into the another. Therefore, the mathematical relation for this statement is known as the mass-energy equivalence equation. Moreover, the concept of energy conversion is also applied to understand the significance of this equation.