a ring of rdius 0.1m is made out of a metallic wire of cross section 10^6 m^2.the ring has a uniform charge of pi coulumb.find change in radius of ring when charge of 10^-7coulumb is placed at center of ring

New radius=r
consider the element which substends angle d(theta) at the center. At the two end points of the element tangential tension will be there ---> resolve it -----> only vertical comp. ----> equate this vertical comp.s with the force due to charge particle at the center on the element.

You can do this with other method find out tension with the above method keeping the radius as original one and find out young’s modulus in terms of R and dR. But young’s modulus is not given in the question check the question again.