When the gap is closed without placing any object in the screw gauge whose least count is $0.005\ mm$, the $5^{th}$ division on its circular scale with the reference line on main scale, and when a small sphere is placed reading on main scale advances by $4$ divisions, whereas circular scale reading advances by five times to the corresponding reading when no object was placed. There are $200$ divisions on the circular scale. The radius of the sphere is .......... $mm$
Diffcult
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