In a vernier callipers N divisions of vernier scale coincide with `N-1` divisions of main scale (in which length of one divisions is 1mm). The least count of the instrument should be

Answer

`(3sigma lambda)/(2m in_(0))`

Explanation

Net force on upper half`=((lambdal)/2)(sigma/(2in_(0)))`
Torque on upper half`=((lambdal)/2)xxsigma/(2in_(0))xxl/4`
[`l/4=` distance from hinge point for centre of mass]
total torque on rod
`=(lambdal)/2xxsigma/(2 in_(0))xxl/4xx2=I alpha=(ml^(2))/12 prop :. alpha=(3lambdasigma)/(2m in_(0))`