question_answer

A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at height h = 5 cm. Maximum value of R for a body lo complete the loop successfully is for:

A) 2 cm                                      

B) \[\frac{10}{3}\,cm\]

C) \[\frac{15}{4}\,cm\]                                       

D) \[\frac{18}{3}\,cm\]

Correct Answer: A

Solution :

Key Idea: Energy of body at A is only potential and at B it is only kinetic. Body possess potential energy due to its, height h, this potential energy is used in given kinetic energy to the body \[\therefore \]     \[mgh=\frac{1}{2}mv_{B}^{2}\] Where, \[{{v}_{B}}\]is velocity at B. \[\therefore \]       \[{{v}_{B}}=\sqrt{2gh}\] Also we know that to complete the vertical circle of radius R \[{{v}_{B}}=\sqrt{5gR}\] Equating the two expressions, we get  \[\sqrt{5gR}=\sqrt{2gh}\] \[\Rightarrow \]\[R=\frac{2}{5}h=\frac{2\times 5}{5}=\,2\,cm\]