Question

The main scale, on a travelling microscope, has 20 divisions each between its different ‘centimeter marks’. The vernier scale, attached to it, has 50 divisions and these coincide with 49 divisions of the main scale. The value of one vernier scale division, and the least count of this vernier, are equal, respectively, to 

(1) 0.049 mm and 0.001 mm 

(2) 0.049 mm and 0.001 cm 

(3) 0.049 cm and 0.001 mm 

(4) 0.049 cm and 0.001 cm

Answer 1

Correct option: (4) 0.049 cm and 0.001 cm

Explanation: 

There being 20 divisions, between the ‘centimeter marks’, the value of one main scale division is (1/20) cm = 0.05 cm

Now 50 division, of the vernier, coincide with 49 division of the main scale. Hence value of one vernier scale division is (49 x 0.05/50)cm = 0.049 cm

∴ Least count = 1 (M.S.D) – 1 (V.S.D) = (0.05–0.049) cm 

= 0.001 cm