Diameter of a spherical bob is measured using a vernier callipers. 9 divisions of main scale, in ver

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The diameter of a spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale. One main scale division is $1\, {mm}$. The main scale reading is $10\, {mm}$ and $8^{\text {th }}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04\, {cm}$, then the radius of the bob is $...... \,\times 10^{-2} \,{cm}$

A

$0.52$

B

$520$

C

$5.2$

D

$52$

(JEE MAIN-2021)

Solution

$9 \,{MSD}=10 \,{VSD}$

$9 \times 1\, {mm}=10\, {VSD}$

$\therefore 1 \,{VSD}=0.9\, {mm}$

${LC}=1\, {MSD}-1\, {VSD}=0.1 \,{mm}$

Reading $={MSR}+{VSR} \times {LC}$

$10+8 \times 0.1=10.8\, {mm}$

Actual reading $=10.8-0.4=10.4\, {mm}$

radius $=\frac{{d}}{2}=\frac{10.4}{2}=5.2 \,{mm}$

$=52 \times 10^{-2}\, {cm}$

Standard 11

Physics

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