question_answer

An inclined plane ends into a vertical loop of radius r as shown in figure. If a particle of mass m is released from topmost point. The point C on the track as shown in the figure and centre of circular tack are at same horizontal level. The normal force at point C is-

A) 8 mg                

B)   7 mg

C) 1 mg                

D) 3 mg

Correct Answer: A

Solution :

Apply energy conservation b/w highest point & pt C, \[mg\times 4r=\frac{1}{2}m{{v}^{2}}\] \[v=\sqrt{8gr}\] \[N\,\,=\,\frac{m{{v}^{2}}}{R}\,\,at\,\,po\operatorname{int}\,\,C\] \[N\,\,=\,\,8mg\]