The length of a cylinder measured by a Vernier caliper is given by the following observations: $3.29 \, cm, 3.28 \, cm, 3.29 \, cm, 3.31 \, cm, 3.28 \, cm, 3.27 \, cm, 3.29 \, cm, 3.30 \, cm$. The most accurate length of the cylinder is ........ $cm$.

Identify the physical quantity that cannot be measured using a spherometer:

Which of the following is the most precise device for measuring length:
$A)$ a vernier callipers with $20$ divisions on the sliding scale
$B)$ a screw gauge of pitch $1 \; mm$ and $100$ divisions on the circular scale
$C)$ an optical instrument that can measure length to within a wavelength of light?

$A$ Vernier calipers has $1 \,mm$ marks on the main scale. It has $20$ equal divisions on the Vernier scale which match with $16$ main scale divisions. For this Vernier calipers, the least count is (in $\,mm$)

Diameter of a steel ball is measured using a Vernier callipers which has divisions of $0.1\,cm$ on its main scale $(MS)$ and $10$ divisions of its vernier scale $(VS)$ match $9$ divisions on the main scale. Three such measurements for a ball are given as:

$S$.No.	$MS\;(cm)$	$VS$ divisions
$(1)$	$0.5$	$8$
$(2)$	$0.5$	$4$
$(3)$	$0.5$	$6$

If the zero error is $-0.03\,cm,$ then the mean corrected diameter is ........... $cm$.

The least count of a vernier caliper is $\frac{1}{20N} \text{ cm}$. The value of one division on the main scale is $1 \text{ mm}$. Then the number of divisions of the main scale that coincide with $N$ divisions of the vernier scale is: