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Asked by Www.manashjyoti333 9th November 2019, 9:01 PM
Figure shows the tension force acting on the wire at A ( lowest position) and also at B (top most posiion )

At top most position B, we have , Tt + mg = ( mvt2 )/R   .................(1)

Tension in wire when the mass is at B,  Tt = ( mvt2 )/R  - mg ...............(2)

To complete the circular motion in vertical plane, Tt = [ ( mvt2 )/R  - mg ] ≥ 0  or  vt2 ≥ ( R g )  ........................(3)

Let vo be the velocity of circulating mass at position A.

By conservation of energy, we have, (1/2)mvo2 = (1/2)m vt2 + (m g 2R)  ......................(4)

Using eqn.(3) and eqn.(4), vo2 = 5gR  ............................(5)

Strain in the wire when the mass is at A is given by,   Y = ( Tb / A ) / Strain  ....................(6)

where Y is Young's modulus , Tb is tension in the wire and A is area of cross section of wire

at position-A, by force balance, we have,   Tb - mg = ( m vo2 /R )  .................(7)

Using, eqns.(5), (6) and (7), we get, Strain = 6mg / ( A Y )
Answered by Expert 10th November 2019, 8:29 AM
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