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A metabollic rod of unknown radius was h...

A metabollic rod of unknown radius was held in between the lower jaws of a vernier callipers. The main scaleis divided into millimetres and the venier scale has 50 divisions. The vernier coincinding division is 39. If the zeroth division of the vernier scale lies between 6.3 cm and 6.4 cm of the main scale, find the radius.

Text Solution

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Number of V.S.D., N = 50
V.C.D. = 39
M.S.R. = 6.3 cm = 63 mm
Diameter of the metallic rod = 2R + V.C.D x L.C.
`rArr = (MSR + VCD xx LC)/(2)`
L.C. of the vernier callipers, L.C.
` = (1MSD)/(N) = (1mm)/(50) = (0.1)/(5) = 0.02 mm`
Diameter = 65 mm + 39 x 0.02 mm = (63 +0.78) mm
D = 63.78 mm (or) D 6.378 cm
` therefore ` Radius of the given rod,
`R = D/2 = (6.378)/(2) = 3.189 cm = 31.89 mm`
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