Answer :
Final answer:
The question requires the application of Einstein's theory of energy-mass equivalence to predict the mass required to sustain the body's power needs. From our calculations, none of the options offered match the calculated amount of mass required (1.57*10⁻⁷ mg). Further information or corrections in the question might be necessary for an accurate answer.
Explanation:
To find the amount of mass needed to sustain the body's power needs, we will use the equivalence of mass-loss and energy conversion, as well as the body's power consumption rate.
From Einstein's famous equation E=mc², where E is energy, m is mass, and c is the speed of light, we can deduce that mass can be converted into energy. Given that the body's power need is 100 Watts (which is equivalent to 100 Joules of energy per second), and 0.7% of body's mass could be converted into energy, we can solve for the required mass.
Let's define the mass that would be converted into energy in a second as 'm'. This mass would produce 100 Joules energy in this second, so we have 100 = m*c². Solving for m, and knowing that c = 3*10⁸ m/s, we would have m = 100 / (9*10¹⁶). This gives m = 1.1*10⁻¹⁵ kg.
But this 'm' is only 0.7% of the required mass of the body according to the condition. Therefore, the total required mass would be m_total = m / 0.007 = 1.1*10⁻¹⁵ / 0.007 = 1.57*10⁻¹³ kg.
However, we generally deal with bigger units than kg for mass in such topics. Therefore, let's convert this result from kg to mg (1 kg = 10⁶ mg): m_total = 1.57*10⁻¹³ * 10⁶ = 1.57*10⁻⁷ mg.
Looking at the given options, none of them matches with our calculated value. Therefore, there might be a mistake in the question itself or we might need to consider more specific details for the energy-mass conversion process in the human body.
Learn more about Energy-mass equivalence here:
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