Respuesta :
Answer:
D. 5.18 x 10⁻¹²
Explanation:
[tex]\frac{dE}{dt}[/tex] = rate at which sun radiates energy = 3.92 x 10²⁶ W
M = mass of sun = 1.99 x 10³⁰ kg
[tex]\frac{dm}{dt}[/tex] = rate at which sun's mass is lost
c = speed of light
Energy is given as
E = m c²
Taking derivative both side relative to "t"
[tex]\frac{dE}{dt}=c^{2}\frac{dm}{dt}[/tex]
[tex]3.92\times 10^{26}=(3\times 10^{8})^{2}\frac{dm}{dt}[/tex]
[tex]\frac{dm}{dt}[/tex] = 4.4 x 10⁹ kg/s
t = time interval = 75 yrs = 75 x 365 days = 75 x 365 x 24 hours = 75 x 365 x 24 x 3600 sec = 2.4 x 10⁹ sec
[tex]m[/tex] = mass lost
mass lost is given as
[tex]m = t\frac{dm}{dt}[/tex]
[tex]m = (2.4\times 10^{9})(4.4\times 10^{9})[/tex]
m = 10.56 x 10¹⁸ kg
fraction is given as
fraction = [tex]\frac{m}{M}[/tex]
fraction = [tex]\frac{10.56\times 10^{18}}{1.99\times 10^{30}}[/tex]
fraction = 5.18 x 10⁻¹²
