I am a vernier calipers. I have a task to measure the length of a pencil as shown in the figure. The vernier constant of my vernier scale is 0.05 times the value of one division of main-scale. My Vernier Scale has n-divisions and coincides with (n – 4) divisions of main scale. While measuring the length of pencil, the n5 th division of Vernier-Scale exactly coincides with a division of main-scale. Neglect any zero error.Now choose the correct option(s)
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a
The value of n is 40
b
The vernier constant of Vernier scale is 0.005 cm
c
The length of Pencil is 8.44 cm
d
The length of Pencil is 8.48 cm
answer is B.
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Detailed Solution
L.C.=0.05 times 1MSD=0.05×0.1cm=0.005 cm=0.05mmLet 1 V.S.D.=x∴L.C.=1M.S.D.−1 V.S.D.⇒ 0.05mm=1mm−x⇒x=0.95 mmGiven : (n−4)×1mm=n×0.95mm⇒ n=80 Length of pencil =8.4cm+[0.005cm×(805)]=8.48 cm