Q11 of 39 Page 300

A steel wire of original length 1 m and cross-sectional area 4.00 mm2 is clomped at the two ends so that it lies horizontally and without tension. If n load of 2.16 kg is upending from (he middle point of the wire, what would be its vertical depression? Y of the steel = 2.0 × 1011 N m-2. Take
g 10 m s-2.

1.5 cm

Given, length of the wire,


Cross-sectional area,


Weight of the load,


Young modulus of the wire,



Let T define the tension in the wire due to the load.


Now, from the figure,



Expanding using binomial theorem,



We know, , hence



The new length is given by while the original length is AB. Hence, the change in length is




The Young’s modulus is given by




Now, we balance the forces.






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