Question

what is the energy equivalent of an object with a mass of 2.5 kg?
○ 5.5 × 10⁸ j
○ 7.5 × 10⁸ j
○ 3.6 × 10¹⁶ j
○ 2.25 × 10¹⁷ j

Explanation:

Step1: Recall the mass - energy equivalence formula

The mass - energy equivalence formula is given by \(E = mc^{2}\), where \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light in a vacuum. The value of \(c=3\times 10^{8}\space m/s\).

Step2: Substitute the given values into the formula

We are given that \(m = 2.5\space kg\) and \(c = 3\times10^{8}\space m/s\). Substitute these values into the formula \(E=mc^{2}\):

\[

$$\begin{align*} E&=2.5\space kg\times(3\times 10^{8}\space m/s)^{2}\\ &=2.5\space kg\times9\times 10^{16}\space m^{2}/s^{2}\\ &=(2.5\times9)\times 10^{16}\space J\\ & = 22.5\times 10^{16}\space J\\ &=2.25\times 10^{17}\space J \end{align*}$$

\]

Answer:

\(2.25\times 10^{17}\space J\) (the option with \(2.25\times 10^{17}\space J\))