A sphere of mass 4 ~kg is attached to one end of a steel wire of length 1 ~m and radius 1 ~mm . It is whirled in a vertical circle with an angular velocity 10 rad s ⁻¹ . If the sphere is at the lowest point of its path, the elongation in the wire is ____ ( g =10 ~ms ⁻², Y _ steel =20 10¹⁰ Nm ⁻² )