Not true. If you formed a closed loop with your finger, through the handle, you could lift it up. This would work even if the loop had a gap which was narrower than the thinnest part of the handle. The cup would rotate around the finger so that some of the contents would spill out, but that is not relevant to the question.
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Without friction, it would be challenging to grip the cup of tea securely, and it might slip from your hand due to the lack of frictional force providing a counteracting force to your grip. This could result in difficulty picking up the cup or holding it steadily.
A cup is greater than an ounce. There are 8 ounces in a cup.
The solubility of sugar (sucrose) is approx. 2 000 g/L at room temperature; it is a very high solubility. If a cup has 200 mL you can dissolve in it 400 g sugar. Thus a cup full of sugar will absorb a cup full of water without overflowing. You may have to mix the two in a bigger pot, but once dissolve you should be able to pour all the mixture back into the cup that held the sugar.
Yes, a plastic cup is generally lighter than a glass cup because plastic is less dense than glass. This means that a plastic cup will weigh less than a glass cup of the same size.
To convert two thirds of a cup to grams, you would need to know the density of the ingredient being measured. Without this information, it is not possible to provide an accurate conversion.
There are about 5 tablespoons in one third of a cup.