A steel wire of diameter 0.5mm and Young's modulus 2 × 10 ^ 11 N m...

A steel wire of diameter

0.5mm

and Young's modulus

2 \times {10}^{11}N{m}^{- 2}

carries a load of mass M. The length of the wire with the load is 1.0 m. 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 1.0 mm, 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. If the load on the steel wire is increased by

1.2kg

, the vernier scale division which coincides with a main scale division is __________. Take

g = 10m{s}^{- 1}and\pi = 3.2 .

Correct answer

Step-by-step solution

d = 0.5mm

Y = 2 \times {10}^{11}

l = 1m

∆ l = \dfrac{Fl}{Ay} = \dfrac{mgl}{\dfrac{\pi{d}^{2}}{4}y} = \dfrac{1.2 \times 10 \times 1}{\dfrac{\pi}{4} \times {\left(5 \times {10}^{- 4}\right)}^{2} \times 2 \times {10}^{11}}

∆ l = \dfrac{1.2 \times 10}{\dfrac{3.2}{4} \times 25 \times {10}^{- 8} \times 2 \times {10}^{11}}

= \dfrac{12}{1.6 \times 25 \times {10}^{3}} = \dfrac{12}{40 \times {10}^{3}} = 0.03mm

So 3^rd division of vernier scale will coincicle with main scale

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