Consider a vernier calliper in which each 1cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the vernier calliper, 5 divisions of the vernier scale coincides with 4 divisions of main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale.
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a
If the least count of screw gauge is 0.005 mm, then the ratio of the pitch of screw gauge to least count of the vernier calliper is 2
b
If the least count of screw gauge is 0.01 mm, then the ratio of pitch of the screw gauge and least count of vernier calliper is 2
c
If the least count of screw gauge is 0.01 mm then the ratio of least count of the linear scale of the screw gauge to least count of vernier calliper is 2
d
If the least count of screw gauge is 0.005 mm, then the ratio of the least count of the linear scale of the screw gauge to least count of the vernier calliper is 2
answer is A.
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Detailed Solution
1MSD=18cm; 5VSD=4MSD1VSD=45MSD=45×18=110 cmLeast count of vernier caliper =1MSD−1VSD=18 cm−110 cm=0.025 cmPitch of scres gauge P=L⋅C 100If L⋅C=0.005 mm, then P=0.5 mmNow PL⋅C of vernier callipers=0.5 mm0.025 cm=2So option A is correctIf L.C of screw gauge = 0.01 mm, then P = 1 mmNow L.C of linear scale of screw gauge =P2=0.5 mm P/2L⋅C of V⋅C=0.5 mm0.025 cm=2So option C is correct