Discussion Forum

A steel wire of diameter 0.5 mm and Young's modulus 2 × 10¹¹ 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 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 1.2 kg, the vernier scale division which concides with a main scale division is ...........   Take , g= 10 m s^-1 and π =3.2)

Answer:

Explanation:

Given , d= 0.5mm

   Y = 2 × 10¹¹   Nm^-2 

   l= 1 m

  $\triangle l= \frac{Fl}{AY}= \frac{mgl}{\frac{\pi d^{2}}{4}}Y$

    =   $\frac{1.2 \times 10 \times 1}{\frac{\pi}{4}\times (5\times 10^{-4})^{2}\times2\times 10^{11}}$

   = 0.3 mm

  LC of vernier = $(1-\frac{9}{10})mm = 0.1mm$

   So, 3rd division of vernier scale will coincide with main scale.