Question

Students $A,B$ and $C$ measure the length of a room using $25m$ long measuring tape of least count (LC) $0.5cm$, meter-scale of LC $0.1cm$ and a foot-scale of $LC0.05cm$, respectively. If the specified length of the room is $9.5m$, then which of the following students will report the lowest relative error in the measured length ?

• A. Student A
• B. Student B
• C. Student C
• D. Both, student B and C

Answer 1

Answer: (A)

Student $A$: Length of scale $=25m$
Least count $=0.5cm=0.005m$
Student $A$ can measure the length of $9.5m$ by using the scale only once so there will be an error of $0.005m$ in $9.5m$
$\therefore$ Relative error $=\frac{0.005}{9.5}=0.0005$
Student $B$ : Length of scale : $1m=100cm$
Least count $=0.05cm$
To measure $9.5m$, student $B$ has to use this meter scale atleast $10$ times
$\therefore$ Relative error $=\frac{0.05}{100}\times 10=0.005cm$
Student $C$ : Length of scale : 1 foot $=30.48cm$
Least count $=0.05cm$
To measure $9.5m$, student $C$ has to use this scale approximately $31$ times
$\therefore$ Relative error $=\frac{0.05}{30.48}\times 31=0.05cm$
$\therefore$ Relative error is least for Student $A$.