Question Video: Finding the Total Mass of Two Objects While Combining Uncertainties | Nagwa Question Video: Finding the Total Mass of Two Objects While Combining Uncertainties | Nagwa

Question Video: Finding the Total Mass of Two Objects While Combining Uncertainties Physics • First Year of Secondary School

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If the mass of object A is (3 ± 0.02) kg and the mass of object B is (800 ± 30) g, then the total mass of the two objects equals ＿.

02:05

Video Transcript

If the mass of object A is three plus or minus 0.02 kilograms and the mass of object B is 800 plus or minus 30 grams, then the total mass of the two objects equals blank. (A) 3.8 plus or minus 30.02 kilograms, (B) 830 plus or minus 0.05 kilograms, (C) 3.8 plus or minus 0.05 kilograms, (D) 830 plus or minus 30.02 kilograms.

We want to figure out which of these four answer options correctly fills in the blank. In this question, we’re adding together the masses of two objects, object A and object B. Let’s call the mass of object A 𝑚 sub A and the mass of object B 𝑚 sub B.

We can notice that these two masses are expressed in different mass units, kilograms and grams. We also see that all four of our answer options are given in units of kilograms. This tells us that before we combine these masses, we’ll want to convert the mass of object B into units of kilograms. Because one gram is equal to 10 to the negative three or one one thousandth of a kilogram, we can write 𝑚 sub B as 800 plus or minus 30 all multiplied by 10 to the negative three kilograms. If we multiply through by 10 to the negative three, we can see that the mass of object B can be expressed as 0.8 plus or minus 0.03 kilograms.

It will now be more straightforward to add together these two masses 𝑚 sub A and 𝑚 sub B. When we combine them, three plus 0.8 gives 3.8, and then 0.02 plus 0.03 is equal to 0.05. The total mass of these two objects then expressed in units of kilograms is 3.8 plus or minus 0.05 kilograms. We note that this agrees with answer choice (C).

Our completed sentence reads if the mass of object A is three plus or minus 0.02 kilograms and the mass of object B is 800 plus or minus 30 grams, then the total mass of the two objects equals 3.8 plus or minus 0.05 kilograms.

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