The L.C of a vernier calliper is 0.01 cm and its zero error is -0.03 cm while measuring the length of a rod. The main scale reading is 4.6 cm and the sixth division on the vernier is in line with a marking on the main scale, then what will be the length of the rod?

Hint
Vernier calliper LC is calculated by dividing the smallest reading of the main scale with the total number of divisions of the vernier scale. The difference between one smallest reading of the main scale and one smallest reading of vernier scale which is 0.1 mm or 0.01 cm. Due to both systematic and random errors the least count error occurs.

Complete step by step answer
Main scale reading $MSR= 4.6cm$
Vernier calliper scale $V.C = 6$
L.C of vernier calliper $= 0.01 cm$
Zero error $= -0.03 cm$
Observed reading $=MSR+(V.C\times L.C)$
Substituting the value, we get;
$\Rightarrow 4.6+(6\times 0.01)$
$\Rightarrow 4.66$
Formula to calculate length of rod
Length of the rod = observed reading - zero error
Substituting the value of observed reading and zero error
$\Rightarrow 4.66 - (-0.03)$
$\Rightarrow 4.66 +0.03$
$\Rightarrow 4.69 cm.$

Note
Vernier calliper is a measuring device which contains a main scale with a fixed jaw and a sliding jaw with an attached vernier. It is used to precisely measure linear dimensions. Vernier callipers, like micrometres, are the tools more commonly used for low tolerance measuring. Low tolerance measuring tools provide very accurate measurements, with a small margin for error. Applications of vernier calliper machine shop, medical instruments, research applications, educational institutions. Principle of the vernier calliper is that the divisions on the vernier scale are such that the length of (n) divisions on the vernier scale is equal to (n-1) divisions of the main scale.