A small sphere tied to the string of length 0.7 m is describing a vertical circle so that the maximum and minimum tensions in the strings are in the ratio 
. What will be the velocity of the sphere (in metre 
) at the lowest position. 
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(7) Let 
and 
be the speeds of sphere at the bottom and the top positions and 
be the mass.
tension at the bottom or the maximum tension
tension at the top or the minimum tension
Using conservation of energy,
Loss in 
from bottom to the top = Gain in GPE
Using (i) and (ii), we get 
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