In a Vernier calipers, 50 divisions of Vernier scale coincides with 47 divisions of main scale. There is no zero error in the device. When an object of length $l = 7.62 m m$ is placed between the lower jaws of the calipers, ${(25 + N)}^{t h}$ division of main scale exactly coincides with $M^{t h}$ division of Vernier scale. Find N. (Given value of 1 main scale divisions is 1 mm and number of Vernier scale divisions is 50)

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Detailed Solution

$x + M V S D = (18 + N) M S D$

$50 V S D = 47 M S D$

$1 V S D = \frac{47}{50} M S D = 0.94 M S D$

$G i v e n x = 0.62 m m$

$(18 + N) M S D - M V S D = 7.62 m m$

$18 + N - M (0.94) = 0.62$

M must be an integer
Now option $A \Rightarrow N = 8, M = 27$
$O p t i o n B \Rightarrow N = 2, M = 20.65 (W r o n g)$

$O p t i o n C \Rightarrow N = 3, M = 21.7 (W r o n g)$

$O p t i o n D \Rightarrow N = 1, M = 19.55 (W r o n g)$

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