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

The correct option is 100.

Let us solve the problem step-by-step by converting the given mass to volume based on the standard density of water.

Step 1: Convert the weight of water into grams
We are given that 1 litre of water weighs 1 kg.
Since $1\text{ kg}=1000\text{ g}$, we can write:
$1000\text{ g of water}=1\text{ litre}$

Step 2: Convert litres to cubic millimetres (mm³)
Recall the volume unit conversions:
$1\text{ litre}=1000\text{ cm}{3}^{}$
Since $1\text{ cm}=10\text{ mm}$, cubing both sides gives:
$1\text{ cm}{3}^{}={\left(10\text{ mm}\right)}^3=1000\text{ mm}{3}^{}$
Therefore, 1 litre in cubic millimetres is:
$1\text{ litre}=1000\times 1000\text{ mm}{3}^{}={10}^6\text{ mm}{3}^{}$

Step 3: Relate mass in grams directly to volume in cubic millimetres
From Step 1 and Step 2:
$1000\text{ g of water}={10}^6\text{ mm}{3}^{}$
Dividing both sides by 1000, we find the volume of 1 g of water:
$1\text{ g of water}=1000\text{ mm}{3}^{}$

Step 4: Calculate the volume for 0.1 g of water
Multiply both sides by 0.1:
$0.1\text{ g of water}=0.1\times 1000\text{ mm}{3}^{}=100\text{ mm}{3}^{}$

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