$A$ vernier callipers used by a student has $20$ divisions in $1\;cm$ on the main scale. $10$ vernier divisions coincide with $9$ main scale divisions. When the jaws are closed,the zero of the main scale is to the left of the zero of the vernier scale,and the $6^{th}$ division of the vernier scale coincides with a main scale division. The student places a wooden cylinder between the jaws to measure its length. The zero of the vernier scale is to the right of the $3.20\;cm$ mark,and the $8^{th}$ vernier division coincides with a main scale division. When measuring the thickness (diameter) of the cylinder,the zero of the vernier scale lies to the right of the $1.50\;cm$ mark,and the $6^{th}$ vernier division coincides with a main scale division. The correct values of the 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
    $3.270\;cm, 1.560\;cm$

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The internal and external diameters of a hollow cylinder measured with vernier calipers are $(5.73 \pm 0.01) \text{ cm}$ and $(6.01 \pm 0.01) \text{ cm}$ respectively. Then the thickness of the cylinder wall is

Two full turns of the circular scale of a screw gauge cover a distance of $1 \ mm$ on its main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $-0.03 \ mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3 \ mm$ and the number of circular scale divisions in line with the main scale as $35$. The diameter of the wire is ....... $mm$

In a screw gauge, when the circular scale is given five complete rotations, it moves linearly by $2.5 \text{ mm}$. If the circular scale has $100$ divisions, the least count of the screw gauge is . . . . . . $\text{mm}$.

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \text{ mm}$. 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 conditionMain scale readingCircular 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

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$A$ student performs an experiment of measuring the thickness of a slab with a vernier calliper whose $50$ divisions of the vernier scale are equal to $49$ divisions of the main scale. He noted that the zero of the vernier scale is between $7.00 \; cm$ and $7.05 \; cm$ mark of the main scale and the $23^{rd}$ division of the vernier scale exactly coincides with the main scale. The measured value of the thickness of the given slab using the calliper will be (in $; cm$)

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