Question

Diameter of a wire measured by a screw guage in four different readings is found to be 2.20 mm, 2.10 mm, 2.40 mm and 1.90 mm.

• A. Number of significant figures in all readings is two.
• B. Error in $1^{st}$ reading is negative.
• C. Mean error of readings is zero.
• D. Error in $4^{th}$ reading is 0.25 mm.

Answer 1

Answer: (B), (D)

The correct options are
B Error in $1^{st}$ reading is negative.
D Error in $4^{th}$ reading is 0.25 mm.

True diameter is, $D=\frac{D_1+D_2+D_3+D_4}{4}=\frac{2.2+2.1+2.4+1.9}{4}$
D =2.15 mm
$\Delta D_1=D-D_1=2.15-2.20=-0.05$
$\Delta D_4=D-D_4=2.15-1.90=0.25$
$\Delta D_{mean}=\frac{|\Delta D_1|+|\Delta D_2|+|\Delta D_3|+|\Delta D_4|}{4}=0.15$
Number of significant figures is 3 in each of the cases.