QJEEM25Ph1098: JEE Main 2025 Physics - Class 11 JEEM25Ph1098 Solution: Given below are two statements : Statement I: In a vernier…

Statement I: “In a vernier callipers, one vernier scale division is always smaller than one main scale division.”

In a standard (direct) vernier caliper, $n$ divisions on the vernier scale coincide with $(n-1)$ divisions on the main scale.

Consequently, each vernier scale division is slightly smaller than each main scale division so that the offset (or “least count”) can be read via how they coincide when taking measurements.

Thus, for a direct vernier, one vernier scale division is indeed smaller than one main scale division.

Therefore, Statement I is true for a typical (direct) vernier caliper.

Statement II: “The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.”

The usual formula for the least count (vernier constant) in a direct vernier is

$\text{Least Count} \;=\; \bigl(\text{value of 1 main scale division}\bigr) \;-\; \bigl(\text{value of 1 vernier scale division}\bigr).$

Alternatively, if $n$ vernier divisions coincide with $(n-1)$ main-scale divisions, then

$\text{Least Count} \;=\; \frac{\text{value of 1 main scale division}}{n}.$

The statement claiming the vernier constant is the product of (1 main scale division) and (number of vernier scale divisions) is incorrect.

Therefore, Statement II is false.