Question

If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

• A. $(0.94\pm 0.03)\text{cm}$
• B. $(0.94\pm 0.01)\text{cm}$
• C. $(0.94\pm 0.02)\text{cm}$
• D. $(0.94\pm 0.04)\text{cm}$

Answer 1

The correct option is C $(0.94\pm 0.02)\text{cm}$

Given,
$L_A=(3.25\pm 0.01)\text{cm}=L_{A_{mean}}\pm \Delta L_{A_{mean}}$
$L_B=(4.19\pm 0.01)\text{cm}=L_{B_{mean}}\pm \Delta L_{B_{mean}}$
So, $L_B-L_A=(L_{B_{mean}}-L_{A_{mean}})\pm (\Delta L_{A_{mean}}+\Delta L_{B_{mean}})$
[In addition or subtraction, the mean absolute error is added]
$\Rightarrow L_B-L_A=\left[\right(4.19-3.25)\pm (0.01+0.01\left)\right]\text{cm}$
$\Rightarrow L_B-L_A=(0.94\pm 0.02)\text{cm}$