The diameter of a spherical bob is measured using a vernier calli… - Vidyadip

MCQ

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
$5.2$
✓
$52$

✓

Answer

Correct option: D.

$52$

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

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

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

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

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

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

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

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

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

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