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 Einstein's mass - energy equivalence formula

The formula is \(E = mc^{2}\), where \(m\) is the mass of the object and \(c\) is the speed of light (\(c=3\times 10^{8}\space m/s\)).

Step2: Substitute the given values into the formula

Given \(m = 1.83\space kg\) and \(c = 3\times 10^{8}\space m/s\). Then \(E=(1.83)\times(3\times 10^{8})^{2}\).
First, calculate \((3\times 10^{8})^{2}=9\times 10^{16}\).
Then \(E = 1.83\times9\times 10^{16}\).
\(1.83\times9=16.47\).
So \(E=16.47\times 10^{16}\).
In scientific notation \(E = 1.647\times 10^{17}\approx1.65\times 10^{17}\space J\).

Answer:

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