One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text{th}}$ division of the main scale coincides with $(n+1)^{\text{th}}$ division of the vernier scale,the least count of the vernier caliper is:

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

The length of a cylinder is measured with the help of vernier callipers whose nine divisions of the main scale are equal to ten divisions of the vernier scale. The smallest division on the main scale is $0.5 \ mm$. It is observed that the zero of the vernier scale has just crossed the $78^{th}$ division of the main scale,and the fourth division of the vernier scale coincides with a main scale division. The length of the cylinder is $..... \ mm$.

$A$ screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw gauge,the state of the instrument is shown by diagram $(I)$. When both the rods are inserted together in series,the state is shown by diagram $(II)$. What is the zero error of the instrument in $mm$? Given: $1 \, M.S.D. = 100 \, C.S.D. = 1 \, mm$.

$A$ specially designed Vernier calliper has the main scale least count of $1 \,mm$. On the Vernier scale,there are $10$ equal divisions and they match with $11$ main scale divisions. Then,the least count of the Vernier calliper is ........... $mm$.

The vernier scale of a travelling microscope has $50$ divisions which coincide with $49$ main scale divisions. If each main scale division is $0.5 \ mm$,calculate the minimum inaccuracy in the measurement of distance. (in $mm$)