A body slides down a frictionless track which ends in a circular loop of diameter D. Then the minimu

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A body slides down a frictionless track which ends in a circular loop of diameter D. Then the minimum height $h$ of the body in terms of D so that it may just complete the loop, is\

Professor PC Thomas Classes · Answer

KE at $\mathrm{B}=\mathrm{PE}$ at A\ $\frac{1}{2} m v^{2}=m g h$ $$ \begin{equation*} \mathrm{v}_{1}^{2}=2 \mathrm{gh} 	ag{1} \end{equation*} $$ This is the square of the velocity acquired while reaching B. But the velocity required for circular motion in a vertical circle is\ $\mathrm{v}_{1}=\sqrt{5 R g}$\ $\mathrm{v}_{1}=\sqrt{5\left(\frac{D}{2}ight) g}$ $$ \begin{equation*} v_{1}^{2}=5 \frac{D}{2} g 	ag{2} \end{equation*} $$ where D is the diameter\ From (1) \& (2) $2 \mathrm{gh}=5 \frac{D}{2} g$\ $\mathrm{h}=$\