A vernier callipers used by student has $20$ divisions in $1\;cm$ on main scale. $10$ vernier divisions coincide with $9$ main scale divisions. When jaws are closed, zero of main scale is on left of zero of vernier scale and $6\ th$ division of vernier scale coincides with any of main scale divisions. He places a wooden cylinder in between the jaws and measures the length. The zero of vernier scale is on right of $3.20\;cm$ and $8\ th$ vernier division coincides with any main scale division. When he measures thickness of cylinder he finds that zero of vernier scale lies on right of $1.50\;cm$ mark of main scale and $6\ th$ division of vernier scale coincides with any main scale division. The correct values of measured length and diameter are respectively
- A$3.21\ cm,$ $1.50$ $cm$
- B$3.210$ $cm,$ $1.500$ $cm$
- C$3.27$ $cm,$ $1.93$ $cm$
- D$3.270$ $cm,$ $1.560$ $cm$
Similar Questions
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:
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:
- [JEE MAIN 2024]
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 \mathrm{~mm}$ and circular scale reading is equal to $42$ divisions. Pitch of screw gauge is $1 \mathrm{~mm}$ and it has $100$ divisions on circular scale. The diameter of the wire is $\frac{x}{50} \mathrm{~mm}$. The value of $x$ is :
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 \mathrm{~mm}$ and circular scale reading is equal to $42$ divisions. Pitch of screw gauge is $1 \mathrm{~mm}$ and it has $100$ divisions on circular scale. The diameter of the wire is $\frac{x}{50} \mathrm{~mm}$. The value of $x$ is :
- [JEE MAIN 2024]
If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5 \mathrm{~mm}$, the Vernier constant of travelling microscope is:
If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5 \mathrm{~mm}$, the Vernier constant of travelling microscope is:
- [JEE MAIN 2024]
In a Vernier Calipers. $10$ divisions of Vernier scale is equal to the $9$ divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of $zero$ of the main scale and $4^{\text {th }}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $1\,mm$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between $30$ and $31$ divisions of main scale reading and $6^{\text {th }}$ Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be $.......cm$
- [JEE MAIN 2022]
Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.
Measurement condition
Main scale reading
Circular scale reading
Two arms of gauge touching each other without wire
$0$ division
$4$ division
Attempt-$1$: With wire
$4$ division
$20$ division
Attempt-$2$: With wire
$4$ division
$16$ division
What are the diameter and cross-sectional area of the wire measured using the screw gauge?
Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.
| Measurement condition | Main scale reading | Circular scale reading |
| Two arms of gauge touching each other without wire | $0$ division | $4$ division |
| Attempt-$1$: With wire | $4$ division | $20$ division |
| Attempt-$2$: With wire | $4$ division | $16$ division |
What are the diameter and cross-sectional area of the wire measured using the screw gauge?
- [IIT 2022]