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yes TN ranks are usually low when compared to other states barely 10-20 in tn will be in the top indian 1000

for ur second question,
considering a air-resistance free atmosphere, the bob needs a velocity of 0 at the top most position to complete a circle ( since there is no possiblity of tauting)

lets assume that the circle nearly touches the ground .if the radius of the cirle is l. then the total PE at the top is mg(2r).KE = 0 . TE = 2mgl

when it is at the bottommost postition , the entire energy is kinetic

KE = 2mgl
v^2 = 4gl

as for ur first question, since there is a possiblity of tauting the minimum velocity at the topmost position must be sqrt(gl) (:: mv^2 / r = mg). applying energy conservation principle the velocity at the bottim must be sqrt(5gl)

mistake in ur second assesment

TRIANGLE OAD CONGRUENT TO TRIANGLE OBE (SSS)

:. ANGLE OAD = ANGLE OBE..............................2

incorrect as OD = OC and not OD = OE

so the next steps too are bound to be wrong