Question

In a vernier caliper, 20th division on the vernier scale coincides with the 17th division on the main scale. If 1 cm on the main scale is divides into 20 equal parts, then what is the least count of the calipers?
a) 0.0075 cm
b)0.0075 mm
c) 0.75 mm
d) 7.5 cm

answer with a derivation

Answer 1

Answer:

Length of one main scale division 1 M.S.D.=

20

1cm

=0.05 cm=0.5 mm

Since, 20th division of vernier scale coincides with 17th division of main scale.

Least count of vernier callipers, L.C.=1 M.S.D.−

20

17

×M.S.D.

⟹ L.C.=0.5 mm−

20

17

×0.5 mm=0.75 mm

Correct answer is option C.

Answer 2

Given

• In a vernier caliper, 20th division on the vernier scale coincides with the 17th division on the main scale.
• 1 cm on the main scale is divides into 20 equal parts.

To Find

• Least count of the calipers

Solution

Number of division on VS=20

1 cm on Main scale (MS)=20 division

Hence, 1MSD=$\frac{1}{20}$=0.05cm

Least count (LC)=$\frac{1MSD}{No. \: of \: vs \: division}$

$\implies \frac{0.05}{20}$

$\implies0.0025cm$

Therefore, answer= 0.0025cm.

Hope it helps you...