The internal and external radii of a hollow cylinder are measured with the help of a vernier callipers. Their values are $(4.23 \pm 0.01) \, cm$ and $(3.87 \pm 0.01) \, cm,$ respectively. The thickness of the wall of the cylinder is

When both jaws of vernier callipers touch each other, the zero mark of the vernier scale is to the right of the zero mark of the main scale, and the $4^{\text{th}}$ mark on the vernier scale coincides with a certain mark on the main scale. While measuring the length of a cylinder, the observer observes $15$ divisions on the main scale and the $5^{\text{th}}$ division of the vernier scale coincides with a main scale division. The measured length of the cylinder is . . . . . . $mm$. (Least count of Vernier calliper $= 0.1 \ mm$)

The figure below shows a particular position of the Vernier calipers on a centimetre scale. In this position,the value of $x$ shown in the figure is .......... $cm$ (figure is not to scale).

If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5 \,mm$, the Vernier constant of travelling microscope is:

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment,distances are measured by

In a Vernier calipers, when both jaws touch each other, the zero of the Vernier scale is shifted to the right of the zero of the main scale and the $7^{th}$ Vernier division coincides with a main scale division. If the value of $1$ main scale division is $1 \text{ mm}$ and there are $10$ Vernier scale divisions, then the Vernier caliper has