Question

what is the energy equivalent of an object with a mass of 1.83 kg?
○ 1.65 × 10¹⁷ j
○ 2.92 × 10¹⁷ j
○ 3.10 × 10¹⁷ j
○ 5.49 × 10¹⁷ j

Explanation:

Step1: Recall the mass - energy equivalence formula

The mass - energy equivalence is given by the formula \(E = mc^{2}\), 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 \(m = 1.83\space kg\) and \(c = 3\times10^{8}\space m/s\). Substitute these values into the formula \(E=mc^{2}\):

\[

$$\begin{align*} E&=1.83\space kg\times(3\times 10^{8}\space m/s)^{2}\\ &=1.83\times9\times 10^{16}\space J\\ &=16.47\times 10^{16}\space J\\ &=1.647\times 10^{17}\space J\approx1.65\times 10^{17}\space J \end{align*}$$

\]

Answer:

\(1.65\times 10^{17}\space J\) (the first option)