If 1 litre of water weighs 1kg, then how many cubic millimetres of water will weigh 0.1 gm?

Correct Option

Given that 1 litre of water weighs 1 kg.

We establish the following unit conversions:

• 1 kg = 1000 g
• 1 litre = 10⁻³ m³
• Since 1 m = 1000 mm, it follows that 1 m³ = (1000 mm)³ = 10⁹ mm³

Combining these conversions, 1 litre can be expressed in cubic millimetres:

1 litre = 10⁻³ m³ = 10⁻³ (10⁹ mm³) = 10⁶ mm³.

Therefore, 10⁶ mm³ of water weighs 1000 g.

To determine the volume of water that weighs 1 g:

1 g = (10⁶ / 1000) mm³ = 1000 mm³.

To determine the volume of water that weighs 0.1 g:

0.1 g = (1000 / 10) mm³ = 100 mm³.

Thus, 100 cubic millimetres of water will weigh 0.1 gm.

Incorrect Options

Options (1), (2), and (4) are incorrect. The precise calculation, based on the given density and standard unit conversions, demonstrates that 0.1 g of water occupies a volume of 100 mm³. The other options do not align with this derived value.