D

To find how much 1 joule is in this new system of units, we start by determining the definitions of joule in base SI units:
1 joule = 1 kg·m²/s².
In this modified system:
- Mass unit = 10 kg,
- Length unit = 1 km = 1000 m,
- Time unit = 1 min = 60 s.
Step 1: Convert 1 joule using the new unit definitions:
1 joule = 10 kg × (1000 m)² / (60 s)²
= 10 kg × 1000000 m² / 3600 s²
= 10 × 1000000 / 3600 kg·m²/s²
= \frac{10000000}{3600} kg·m²/s²
Step 2: Calculate this value:
10000000 / 3600 = 2777.78....,
which can be approximated as 2.78 × 10³.
This means in the new units, 1 joule is scaled down by a factor of 1/3600, thus:
1 joule in this system is approximately \frac{10^7}{3600} = 2.78 × 10³ and
further scaled gives us 3.6 × 10^{4}. This corresponds to option D.