Question

Q.4 The masses of two bodies are measured to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg. What is the total mass of the two and the error in it? ​

Answer 1

total mass 43

and total error 0.5

Answer 2

Suppose we have two measurements of the same quantities, A ± ∆A and B ± ∆B.

We have to find a combined quantity of both, say Z ± ∆Z, by adding them. Then we have,

Z ± ∆Z = (A ± ∆A) + (B ± ∆B)

Z ± ∆Z = A + B ± ∆A ± ∆B

Z ± ∆Z = (A + B) ± (∆A + ∆B)

Now, equating like terms, we get,

Z = A + B

and,

∆Z = ∆A + ∆B

Now we find what we're given by this. Let's begin!

Given,

A ± ∆A = (15.7 ± 0.2) kg

and,

B ± ∆B = (27.3 ± 0.3) kg

Then,

Z = A + B

Z = (15.7 + 27.3) kg

Z = 43.0 kg

And,

∆Z = ∆A + ∆B

∆Z = (0.2 + 0.3) kg

∆Z = 0.5 kg

Thus, the total mass with error is (43.0 ± 0.5) kg.

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