The problem describes a Vernier caliper. The main scale (M) has divisions of 1/2 mm. 49 divisions on the main scale are divided into 50 divisions on the Vernier scale (V). The image shows the position of the scales for a measurement. Assuming there is no zero error, we need to find the reading.

1. Problem Description

The problem describes a Vernier caliper. The main scale (M) has divisions of 1/2 mm. 49 divisions on the main scale are divided into 50 divisions on the Vernier scale (V). The image shows the position of the scales for a measurement. Assuming there is no zero error, we need to find the reading.

2. Solution Steps

The main scale reading is the last division visible before the Vernier scale's zero mark. From the image, the Vernier scale's zero is slightly beyond the 32nd division on the main scale. Since each division is 1/2 mm, the main scale reading is $32 \times 0.5 = 16$ mm. However, the marking indicates 3cm which equals 30mm plus the additional reading past that, so, we estimate that $30 + 2\times (0.5)= 31$ mm plus some extra length.

The least count of the Vernier caliper can be calculated as the difference between one main scale division and one Vernier scale division.

One main scale division = 0.5 mm.

50 Vernier scale divisions = 49 main scale divisions.

So, one Vernier scale division $= \frac{49}{50} \times 0.5 = \frac{49}{100} = 0.49$ mm.

Least Count $= 0.5 - 0.49 = 0.01$ mm.

The Vernier coincidence is the division on the Vernier scale that aligns with a division on the main scale. From the image, the 20th division on the Vernier scale appears to coincide with a main scale division.

Vernier scale reading = Vernier coincidence $\times$ Least count $= 20 \times 0.01 = 0.20$ mm.

Total reading = Main scale reading + Vernier scale reading. In our case, this would imply that 31 plus the coincidence, makes the total reading approximately

$32.00 + 0.70=32.7$mm

Since the 16th division is near the 32nd mark, the main scale reading = 32mm + reading before the start of division. The 7th division appears to be closest, so the reading would be $32+7 \times 0.01$ which would mean $32.07$ mm.

3. Final Answer

32.70 mm is the best answer that is closer. However, the answer closer is 32.07mm because it seems that we have passed the 32nd division but have not reached the next one. So this is what we should assume based on the answer choices.

The answer is (2) 32.07 mm