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Please solve this problem 

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Asked by Www.manashjyoti333 9th November 2019, 9:01 PM
Answered by Expert
Answer:
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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