Question

The Sun converts 4 × 109 kg of mass to energy every second. How many years would it take the Sun to convert a mass equal to the mass of Earth to energy?

Answer 1

7.665×
`10^7` year

Step-by-step explanation:

It is given that the Sun convert 4×
`10^9` kg of mass into energy every second

We have to find that how much time Sun will take to convert mass of earth into energy

The mass of earth is 9.67×
`10^(24)` so the time required to convert this mass into energy
`=(9.67* 10^(24))/(4* 10^9)=2.417* 10^(15)sec=7.665* 10^7\ year`

So the required time will be 7.665×
`10^7` year

Answer 2

4.74 x 10⁷ yr

Step-by-step explanation:

m = Rate of conversion of mass to energy by sun = 4 x 10⁹ kg/s

t = total time taken to convert mass of earth to energy

M = mass of earth = 5.98 x 10²⁴ kg

Using the equation

M = m t

5.98 x 10²⁴ = (4 x 10⁹) t

t = 1.495 x 10¹⁵ sec

we know that, 1 yr = 3.154 x 10⁷ sec

t = (1.495 x 10¹⁵ sec) (3.154 x 10⁷ sec)⁻¹ yr

t = 4.74 x 10⁷ yr