A screw gauge has some zero error but its val | vedclass

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Question

(C) The least count $(L.C.)$ of the screw gauge is $L.C. = \frac{1 \, mm}{100} = 0.01 \, mm$.Let the actual length of each rod be $\ell$ and the zero

Vedclass · Accepted Answer

$+0.14$

Vedclass · Answer

(C) The least count $(L.C.)$ of the screw gauge is $L.C. = \frac{1 \, mm}{100} = 0.01 \, mm$.Let the actual length of each rod be $\ell$ and the zero error be $x$.From diagram $(I)$,the main scale reading is $2 \, mm$ and the circular scale reading is $12$. The observed reading is $2 + 12 	imes 0.01 = 2.12 \, mm$. Thus,$\ell + x = 2.12 \, mm$.From diagram $(II)$,the main scale reading is $4 \, mm$ and the circular scale reading is $10$. The observed reading is $4 + 10 	imes 0.01 = 4.10 \, mm$. Thus,$2\ell + x = 4.10 \, mm$.Subtracting the first equation from the second: $(2\ell + x) - (\ell + x) = 4.10 - 2.12$,which gives $\ell = 1.98 \, mm$.Substituting $\ell$ into the first equation: $1.98 + x = 2.12$,so $x = 2.12 - 1.98 = 0.14 \, mm$.Since the reading is positive,the zero error is $+0.14 \, mm$.

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