$A$ plano-convex lens of unknown material and unknown focal length is given. With the help of a Spherometer,we can measure the,

The diagrams show readings of a screw gauge. Figure $(i)$ shows the zero error reading when the screw gauge is closed,and figure $(ii)$ shows the reading when the screw gauge is being used to measure the diameter of a ball-bearing. What is the diameter of the ball-bearing in $mm$? There are $50$ divisions on the circular scale.

In an experiment to find out the diameter of a wire using a screw gauge,the following observations were noted:
$(a)$ The screw moves $0.5\,mm$ on the main scale in one complete rotation.
$(b)$ Total divisions on the circular scale $= 50$.
$(c)$ Main scale reading is $2.5\,mm$.
$(d)$ The $45^{\text{th}}$ division of the circular scale is on the pitch line.
$(e)$ The instrument has a $0.03\,mm$ negative zero error.
Then the diameter of the wire is $...........\,mm$.

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?

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 ........ $cm$.

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its $10$ Vernier Scale Divisions $(V.S.D.)$ are equal to its $9$ Main Scale Divisions $(M.S.D.)$. The least division on the $M.S.$ is $0.1 \ cm$ and the zero of $V.S.$ is at $x=0.1 \ cm$ when the jaws of the Vernier callipers are closed. If the main scale reading for the diameter is $M=5 \ cm$ and the number of the coinciding vernier division is $8$,the measured diameter after zero error correction is: (in $cm$)