While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is x/50 mm. The value of x is :

Solution

Physics sir · 3 steps

Find the least count first, then add main scale and circular scale parts, and only then match to x/50.

1. Least count. One full turn moves the screw by the pitch, 1 mm, and that turn has 100 circular divisions. So one division is 1/100 = 0.01 mm.

   d = MSR + CSR × LC = 1 + 42 × 0.01 = 1.42 mm

2. Match the form. Set x/50 = 1.42. Then x = 1.42 × 50 = 71.
3. So. The diameter is 1.42 mm and x = 71, option (b).

The idea to keep. Screw gauge reading is always main scale reading plus circular divisions times least count, where least count is pitch divided by the number of circular divisions.

Answer from the NTA final answer key. Solution by PrepWiser.