question_answer 38)

                  Measure of two quantities along with the precision of respective measuring instrument is                 \[A=2.5\,m\,{{s}^{-1}}\pm 0.5\,m\,{{s}^{-1}}\]                         \[B=0.10\,s\pm 0.01\,s\]                 The value of A B will be                 (a) \[(0.25\pm 0.08)\,m\]             (b) \[(0.25\pm 0.5)\,m\]                 (c) \[(0.25\pm 0.05)\,m\]             (d) \[(0.25\pm 0.135)\,m\]                

Answer:

                  (a)  \[AB=(2.5\times 0.10)\pm \left( \frac{0.5}{2.5}+\frac{0.01}{0.10} \right)(2.5\times 0.10)\]                 \[=0.25\text{ }m\pm 0.08\text{ }m\]                 \[=\left( 0.25\pm 0.08 \right)\text{ }m\]