The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between `5.10cm and 5.15cm` of the main scale. The Vernier scale has `50` divisions equivalent to `2.45 cm`. The `24^(th)` division of the Vernier scale exactly coincides with one of the main scale divisions. the diameter of the cylinder is

Options

A. `5.112 cm`
B. `5.124 cm`
C. `5.136 cm`
D. `5. 148 cm`

Answer

B

Explanation

1 Main scale division MSD `=5.15-5.10= 0.05 cm`
50 divisions of vernier scale are equivalent to 2.45 cm. Hence we can write the following :
1 vernier scale division VSD `=(2.45)/(50)=0.049cm`
Least count of the vernier caliper can be written asa follows :
Lest cout `LC= 1 MSD -1 VSD= 0.05-0.049= 0.001cm`
Main scale reading MSR = 5.10 cm
24th division of vernier scale matches with some main scale division. Final reading can be written as follows :
Reading `=MSR +n xxLC=5.10 +24xx0.001= 5.124cm`
Hence option b is correct.