Question

A body travels uniformly a distance of (13.8 $\pm$ 0.2) m in a time (4.0 $\pm$ 0.3) s. Its velocity with error limits is

• A. (3.5 $\pm$ 0.6) m s^-1
• B. (3.5 $\pm$ 0.3) m s^-1
• C. (6.1 $\pm$ 0.6) m s^-1
• D. (6.1 $\pm$ 0.3) m s^-1

Answer 1

Answer: (B)

(3.5 $\pm$ 0.3) m s^-1

Answer 2

Here, $\mathrm { s } = ( 13.8 \pm 0.2 ) \mathrm { m }$

$\mathrm { t } = ( 4.0 \pm 0.3 ) \mathrm { s }$

$\therefore$Velocity, $\mathrm { v } = \frac { \mathrm { s } } { \mathrm { t } } = \frac { 13.8 } { 4.0 } = 3.45 \mathrm {~ms} ^ { - 1 }$

(Rounded off to first place of decimal

$\therefore \frac { \Delta \mathrm { v } } { \mathrm { v } } = \frac { \Delta \mathrm { s } } { \mathrm { s } } + \frac { \Delta \mathrm { t } } { \mathrm { t } } = \frac { 0.2 } { 13.8 } + \frac { 0.3 } { 4.0 } = \frac { 0.2 } { 13.8 \times 4.0 } = \frac { 4.94 } { 13.8 \times 4.0 }$ $= 0.0895$ $\Delta \mathrm { v } = \mathrm { v } \times 0.0895 = 3.45 \times 0.0895 = 0.3087$

$\therefore$Velocity = $( 3.5 \pm 0.3 ) \mathrm { ms } ^ { - 1 }$