Question

Students $A , B$ and $C$ measure the length of a room using $25\, m$ long measuring tape of least count (LC) $0.5\, cm$, meter-scale of LC $0.1\, cm$ and a foot-scale of $LC 0.05\, cm$, respectively. If the specified length of the room is $9.5 \,m$, 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 $=25 \,m$
Least count $=0.5\, cm =0.005 \,m$
Student $A$ can measure the length of $9.5\, m$ by using the scale only once so there will be an error of $0.005 \,m$ in $9.5 \,m$
$\therefore $ Relative error $=\frac{0.005}{9.5}=0.0005$
Student $B$ : Length of scale : $1 \,m =100 \,cm$
Least count $=0.05 \,cm$
To measure $9.5 \,m$, student $B$ has to use this meter scale atleast $10$ times
$\therefore $ Relative error $=\frac{0.05}{100} \times 10=0.005 \,cm$
Student $C$ : Length of scale : 1 foot $=30.48\, cm$
Least count $=0.05\, cm$
To measure $9.5\, m$, student $C$ has to use this scale approximately $31$ times
$\therefore $ Relative error $=\frac{0.05}{30.48} \times 31=0.05 \,cm$
$\therefore $ Relative error is least for Student $A$.