If the stars at the turnoff point in a star cluster have masses of about four solar masses, how old is the cluster

age of the cluster is 3.125 × 10⁸ years

Explanation:

Given that;

stars at the turnoff point in a star cluster have masses of about 4 solar masses

Age of the cluster?

we know that the main sequence lifetime of a star in solar lifetime(t) is related to the mass of the star in solar masses(M). expressed as

ζ = M^(-5/2)

our M is 4, so we substitute

ζ = 4^(-5/2)

ζ =  0.03125 solar lifetime

now convert the lifetime of star cluster into years

ζ = 0.03125 solar lifetime × (10¹⁰ years / 1 solar lifetime)

ζ = 312,500,000 ≈3.124 × 10⁸ years

therefore age of the cluster is 3.125 × 10⁸ years

another example of kinetic energy would be,

kinetic energy   >     moving energy

answer   >   letter choice (c),   a hammer falling off a table.

hope that !                                         : )