JEE MAIN - Physics (2009 - No. 29)
In an experiment the angles are required to be measured using an instrument, 29 divisions of the
main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the
main scale is half-a degree(=$$0.5^\circ $$), then the least count of the instrument is:
one minute
half minute
one degree
half degree
Explication
30 vernier scale divisions coincide with 29 main scale divisions.
Therefore 1 V.S.D = $${{29} \over {30}}$$ M.S.D
Least count = 1 M.S.D - 1 V.S.D
= 1 M.S.D - $${{29} \over {30}}$$ M.S.D
= $${{1} \over {30}}$$ M.S.D
= $${{1} \over {30}}$$ $$ \times $$ 0.5o
= $${{1} \over {30}}$$ $$ \times $$ $${1 \over 2}$$o
= $${1 \over {60}}$$o
= 1 min
Therefore 1 V.S.D = $${{29} \over {30}}$$ M.S.D
Least count = 1 M.S.D - 1 V.S.D
= 1 M.S.D - $${{29} \over {30}}$$ M.S.D
= $${{1} \over {30}}$$ M.S.D
= $${{1} \over {30}}$$ $$ \times $$ 0.5o
= $${{1} \over {30}}$$ $$ \times $$ $${1 \over 2}$$o
= $${1 \over {60}}$$o
= 1 min