40
410
16
640
The correct option is D
128 kg/m³ = 128 (50 g) / (25 cm)³
= 128 (50 g) / (25 cm)³
= 128 (50 g) / (25/100 m)³
= 128 (50 g) / (1/4 m)³
= 128 (50 g) / (1/64 m³)
= 128 × 50 × 64 g/m³
= 409600 g/m³
To convert to the new units, where the unit of mass is 50 g and the unit of length is 25 cm:
409600 g/m³ = (409600 g/m³) / (50 g / 25 cm)³ = (409600/ (50 g/(25/100 m)³))
= (409600 g/m³) / (50 g / (1/4 m)³)
= 409600 g/m³ / (50 g/ (1/64 m³))
= 409600/(50*64) units
= 409600/3200 units
= 128 units
Let's verify this another way:
128 kg/m³ = 128 (1000 g) / (100 cm)³ = 128000 g/ 1000000 cm³ = 0.128 g/cm³
In the new units, 1 unit of mass = 50 g and 1 unit of length = 25 cm
Therefore, 1 unit of volume = (25 cm)³ = 15625 cm³
Density in new units = (0.128 g/cm³) * (50 g / 1 unit mass) * (1 unit volume / 15625 cm³)
= (0.128 * 50 / 15625) units = 0.0004096 units
There's a discrepancy in the calculation. Let's re-examine the approach.
We have 128 kg/m³. Let's convert this to the new units:
1 kg = 1000 g = 20 units of mass (since 1 unit of mass = 50 g)
1 m = 100 cm = 4 units of length (since 1 unit of length = 25 cm)
1 m³ = (4 units of length)³ = 64 units of volume
So, 128 kg/m³ = 128 * 20 units of mass / 64 units of volume = 40 units of density