The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale. Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading is 1mm and 47^th circular division coincides with the main scale. Find the curved surface area of wire in cm² to appropriate significant figures. ( use $$\pi = {{22} \over 7}$$ )

In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm ( measured by a scale of least count 0.001 cm ) and length is L = 110 cm ( measured by a scale of least count 0.1 cm ). A weight of 50 N causes an extension of X = 0.125 cm (measured by a micrometer of least count 0.001 cm ). Find maximum possible error in the value of Young's modulus. Screw gauge and and meter scale are free from error.

If n^th divisions of the main scale coincide with (n+1)^th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.