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.

Question

Philoid · Accepted Answer

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.