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NEET PHYSICSEasy

The tension in the string revolving in a vertical circle with a mass mm at the end which is at the lowest position is:

A

mv2r\frac{mv^2}{r}

B

mv2rmg\frac{mv^2}{r} - mg

C

mv2r+mg\frac{mv^2}{r} + mg

D

mgmg

Step-by-Step Solution

  1. Identify Forces: At the lowest point of a vertical circle, the forces acting on the mass mm are the tension (TT) in the string acting upwards (towards the center) and the gravitational force (mgmg) acting vertically downwards.
  2. Newton's Second Law: The net radial force towards the center provides the necessary centripetal force (Fc=mv2rF_c = \frac{mv^2}{r}) to maintain the circular path. Fnet=TmgF_{net} = T - mg
  3. Equation of Motion: Equating the net force to the centripetal force: Tmg=mv2rT - mg = \frac{mv^2}{r}
  4. Solve for Tension: T=mv2r+mgT = \frac{mv^2}{r} + mg [Source 75]
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