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Question:

A steel wire of diameter 0.5mm and Young modulus 2×10¹¹ Nm⁻² carries a load of mass M. The length of the wire with the load is 1.0m. A Vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0mm is attached. The 10 divisions of the Vernier scale correspond to 9 divisions of the main scale. Initially, the zero of Vernier scale coincides with the zero of main scale division. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is __________.[Take g =10ms⁻² and π=3.2]

Solution:

d=0.5mm,Y=2×10¹¹,l=1m
Δl=Fl/Ay=mgl/πd²/4y=1.2×10×1/(3.2/4×(5×10⁻⁴)²×2×10¹¹)
Δl=1.2×10×1/(3.2/4×25×10⁻⁸×2×10¹¹)=120/(8×25×10³)=120/(200×10³)=0.6/10³=0.6×10⁻³=0.6mm
So 6th division of vernier scale will coincide with main scale. The solution provided in the input data contains errors in calculation leading to an incorrect answer. The correct calculation is shown above. The 6th division will coincide. If we use π = 3.14, Δl ≈ 0.6mm. Therefore, the 6th division should coincide.