The measurements of two quantities along with | vedclass

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(A) Given: $A = 2.5 \, m/s$,$\Delta A = 0.5 \, m/s$ and $B = 0.10 \, s$,$\Delta B = 0.01 \, s$.We need to find the value of $X = AB$.First,calculate t

Vedclass · Accepted Answer

$(0.25 \pm 0.08) \, m$

Vedclass · Answer

(A) Given: $A = 2.5 \, m/s$,$\Delta A = 0.5 \, m/s$ and $B = 0.10 \, s$,$\Delta B = 0.01 \, s$.We need to find the value of $X = AB$.First,calculate the product: $X = AB = 2.5 	imes 0.10 = 0.25 \, m$.For the propagation of error in multiplication,the relative error is given by: $\frac{\Delta X}{X} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$.Substituting the values: $\frac{\Delta X}{0.25} = \frac{0.5}{2.5} + \frac{0.01}{0.10}$.$\frac{\Delta X}{0.25} = 0.2 + 0.1 = 0.3$.$\Delta X = 0.3 	imes 0.25 = 0.075$.Rounding to the appropriate significant figures,$\Delta X \approx 0.08$.Thus,$AB = (0.25 \pm 0.08) \, m$.

The measurements of two quantities along with the precision of their respective measuring instruments are $A = 2.5 \, m/s \pm 0.5 \, m/s$ and $B = 0.10 \, s \pm 0.01 \, s$. The value of $AB$ will be:

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