A steel wire of diameter $$0.5mm$$ and Young’s modulus $$2$$×$$1011N/m2$$ 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. 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 $$g=10m/s2$$ and π$$=3.2$$ .

Question

A steel wire of diameter  $$0.5mm$$ and Young’s modulus  $$2$$×$$1011N/m2$$  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. 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  $$g=10m/s2$$ and π$$=3.2$$ .

Infinity Learn · Accepted Answer

LC of $$vernier=1-910mm=0.1mm$$ & $$d=0.5mm$$                $$Y=2$$×$$1011Nm-2$$                      $$l=1m$$    Elongation $$=e$$ $$=Fl$$ AY∆$$e=$$∆F l A YΔ$$e=FlAY=mgl$$$$π$$$$d24Y=1.2$$×$$10$$×$$1$$$$π$$$$4$$×$$5$$×$$10$$−$$42$$× $$2$$×$$1011$$Δ$$e=1.2$$×$$103.24$$×$$25$$×$$10$$−$$8$$×$$2$$×$$1011=120.8$$×$$25$$×$$2$$×$$103=1240$$×$$103=0.3mmSince$$ the least count of Vernier caliper is $$0.1mm$$, so $$3rd$$ division of a Vernier scale will coincide with main scale.

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