J & K CET Medical
J & K - CET Medical Solved Paper-2001
question_answer
A body slides without friction from a height h along a track shown in figure, so that it loops the loop in the vertical plane. If the radius of the loop is R, what should be the minimum value of h in terms of R, so that the body is just able to loop the loop. There is no friction between the body and the track :
A) h=R
B) h = 2R
C)\[h=\frac{5}{2}R\]
D) h = 4R
Correct Answer:
C
Solution :
Let v be velocity of the body at C, then \[\frac{m{{v}^{2}}}{R}=mg\] ?.. (i) At A the potential energy is\[mgh\]and at C it is mg (2r). From law of conservation of energy, this loss in potential energy \[mg(h-2R),\]will be equal to kinetic energy of the ball at C, that is \[mg(h-2R)=\frac{1}{2}m{{v}^{2}}\] ...(ii) From Eqs. (i) and (ii), we get \[h=\frac{5}{2}R\]