In finding out refractive index of glass slab the following observations were made through travelling microscope $50$ vernier scale division $=$ $49 \mathrm{MSD} ; 20$ divisions on main scale in each $\mathrm{cm}$ For mark on paper
$\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26$
For mark on paper seen through slab
$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$
For powder particle on the top surface of the glass slab
$\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1$
$(\mathrm{MSR}=$ Main Scale Reading, $\mathrm{VC}=$ Vernier Coincidence)
Refractive index of the glass slab is:
$1.42$
$1.52$
$1.24$
$1.35$
The pitch of the screw gauge is $1\, mm$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is.........$mm$
In a screw gauge, there are $100$ divisions on the circular scale and the main scale moves by $0.5\,mm$ on a complete rotation of the circular scale. The zero of circular scale lies $6$ divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, $4$ linear scale divisions are clearly visible while $46^{\text {th }}$ division the circular scale coincide with the reference line. The diameter of the wire is $...........\times 10^{-2}\,mm$
In a vernier callipers, $10$ divisions of vernier scale coincides with $9$ divisions of main scale, the least count of which is $0.1\,cm$. If in the measurement of inner diameter of cylinder zero of vernier scale lies between $1.3\,cm$ and $1.4\, cm$ of main scale and $2^{nd}$ division of vernier scale coincides with main scale division then diameter will be .......... $cm$
A screw gauge with a pitch of $0.5 \ mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the $45^{th} $division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in $mm$) if the main scale reading is $0.5\ mm$ and the $25^{th}$ division coincides with the main scale line
The diameter of a sphere is measured using a vernier caliper whose $9$ divisions of main scale are equal to $10$ divisions of vernier scale. The shortest division on the main scale is equal to $1 \mathrm{~mm}$. The main scale reading is $2 \mathrm{~cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $8.635 \mathrm{~g}$, thedensity of the sphere $1 \mathrm{~s}$ :