Just at the topmost point of loop take centrifugal force eqal to mg.take out  v^2 term from energy eqn.At 1st only p.e then at the topmost point of loop p.e.+ k.e.

the initial energy of the particle is mgh. It will complete the loop if it reaches the highest point on the loop which has a  height of 2R. therefore by equating mgh =mg2R we get h=2R. R=2.5cm. 

if there is frictional force the radius required will decrease even more depending on the coeff. of friction

Dear mohit,

At the top you have to take centrifugal force to be equal to mg and apply energy conservation law, You will get Maximum value of R=2 cm

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Hi Mohit! For a particle to undergo circular motion,vel at higqest pt=rg^1/2 nd at lowest pt=5rg^1/2 ; proof is simple,at top most point,by balancing the force,we get weight mg= centrifugal forbe mv^2 /r ,now we get v= rg^1/2. At the bottom,K.E = K.E at top + P.E lost ,that is 0.5mv^2 = 0.5 mu^2 + mg(2r) {since,the particle has dropped by a diameter height of 2r},where u= vel at the top most pt nd u= rg^1/2.substituting this,we get v= 5rg^1/2 .NOW BETTER REMEMBER THIS AS FORMULA .now K.E at topmost point= P.E lost ,which means 0.5mv^2= mgh. Substituting v= rg^1/2 nd value of h=5 cm,we get,r = 2h = 10cm. HOPE U R CLEAR WITH THE SOLUTIONS.IF NOT,FEEL FREE 2 CALL ME ON 07209736303. ALL THE BEST, PLZZ APPROVE MY ANSWER IF U LIKE IT

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mgh = 1/2mv2gh = 1/2 * under root 5rg9.8*5*2 / 5*9.8 = rR =2 cm Radius of loop is two cm Jatin Chaudhary VVM, Palanpur