Question

A body is an allowed to slide down a frictionless track from rest position top under gravity. The track ends in a circular loop of diameter D. Then, the minimum height of tile inclined track ( in terms of ) so that it may complete successfully the loop is

• A. 7D/4
• B. 9D/4
• C. 5D/4
• D. 3D/4

Answer 1

Answer: (C)

5D/4

$\text{at point}A\text{for the loop to be completed -}$

$\begin{array}{c}2\frac{m{v}^2}{D}=mg\text{(Foree balancing)}\\ \Rightarrow v^2=\frac{gD}{2}-0\end{array}$

$\begin{array}{c}\text{Foom energy conserwation-}\\ \text{Energy at point}p=\text{Energy at point}A\\ \Rightarrow mgH=mgD+\frac{1}{2}m{v}^2\\ \Rightarrow mgn=mgD+\frac{mgD}{4}\text{from eq}0\\ \Rightarrow H=\frac{5}{4}D\end{array}$