JEE MAIN - Physics (2012 - No. 24)
A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data
58.59 degree
58.77 degree
58.65 degree
59 degree
Explanation
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
Reading of Vernier = Main Scale Reading + Vernier scale reading $$ \times $$ Least count
Given that,
Main Scale Reading = 58.5
Vernier scale reading = 09 division
$$\therefore$$ Reading of Vernier = 58.5o + 9 $$ \times $$ $${{0.5^\circ } \over {30}}$$
= 58.65o
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
Reading of Vernier = Main Scale Reading + Vernier scale reading $$ \times $$ Least count
Given that,
Main Scale Reading = 58.5
Vernier scale reading = 09 division
$$\therefore$$ Reading of Vernier = 58.5o + 9 $$ \times $$ $${{0.5^\circ } \over {30}}$$
= 58.65o
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