there are two vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale…

there are two vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. the vernier scale of one of the calipers ($c_1$) has 10 equal divisions that correspond to 9 main scale divisions. the vernier scale of hte other caliper ($c_2$) has 10 equal divisions that correspond to 11 main scale divisions. the readings of the two calipers are shown in the figure. the measured values (in cm) by calipers $c_1$ and $c_2$, respectively, are 1) 2.87 and 2.87 2) 2.87 and 2.83 3) 2.85 and 2.82 4) 2.87 and 2.86

there are two vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. the vernier scale of one of the calipers ($c_1$) has 10 equal divisions that correspond to 9 main scale divisions. the vernier scale of hte other caliper ($c_2$) has 10 equal divisions that correspond to 11 main scale divisions. the readings of the two calipers are shown in the figure. the measured values (in cm) by calipers $c_1$ and $c_2$, respectively, are 1) 2.87 and 2.87 2) 2.87 and 2.83 3) 2.85 and 2.82 4) 2.87 and 2.86

Answer

Explanation:

Step1: Calculate least - count of $C_1$

Main - scale division (MSD) for both calipers: $1\ MSD=\frac{1}{10}=0.1\ cm$. For $C_1$, 10 Vernier - scale divisions (VSD) = 9 MSD. So, $1\ VSD=\frac{9}{10}\ MSD$. Least - count of $C_1$, $LC_1 = 1\ MSD-1\ VSD=0.1-\frac{9}{10}\times0.1 = 0.01\ cm$.

Step2: Calculate reading of $C_1$

Main - scale reading of $C_1$, $MSR_1 = 2.8\ cm$. Vernier - scale reading of $C_1$, $VSR_1 = 7$. Reading of $C_1$, $R_1=MSR_1+(VSR_1\times LC_1)=2.8+(7\times0.01)=2.87\ cm$.

Step3: Calculate least - count of $C_2$

For $C_2$, 10 VSD = 11 MSD. So, $1\ VSD=\frac{11}{10}\ MSD$. Least - count of $C_2$, $LC_2=1\ VSD - 1\ MSD=\frac{11}{10}\times0.1 - 0.1=0.01\ cm$.

Step4: Calculate reading of $C_2$

Main - scale reading of $C_2$, $MSR_2 = 2.8\ cm$. Vernier - scale reading of $C_2$, $VSR_2 = 3$. Reading of $C_2$, $R_2=MSR_2+(VSR_2\times LC_2)=2.8+(3\times0.01)=2.83\ cm$.

Answer:

  1. 2.87 and 2.83