Answer:
(a) <u>11.3 L</u>
(b) <u>10 M</u>
Explanation:
The mass-luminosity relationship states that:
Luminosity ∝ Mass^3.5
Luminosity = (Constant)(Mass)^3.5
So, in order to find the values of luminosity or mass of different stars, we take the luminosity or mass of sun as reference. Therefore, write the equation for a star and Sun, and divide them to get:
Luminosity of a star/L = (Mass of Star/M)^3.5 ______ eqn(1)
where,
L = Luminosity of Sun
M = mass of Sun
(a)
It is given that:
Mass of Star = 2M
Therefore, eqn (1) implies that:
Luminosity of star/L = (2M/M)^3.5
Luminosity of Star = (2)^3.5 L
<u>Luminosity of Star = 11.3 L</u>
(b)
It is given that:
Luminosity of star = 3160 L
Therefore, eqn (1) implies that:
3160L/L = (Mass of Star/M)^3.5
taking ln on both sides:
ln (3160) = 3.5 ln(Mass of Star/M)
8.0583/3.5 = ln(Mass of Star/M)
Mass of Star/M = e^2.302
<u>Mass of Star = 10 M</u>
