Physics - W.E.P. Question with Solution | TestHub

$mg\mathrm{ }\cos \mathrm{\theta }-N=\frac{m{v}^2}{R};\mathrm{ }N=mg \cos \mathrm{\theta }-\frac{m{v}^2}{R}$

$N=0\Rightarrow mg\mathrm{ }\cos \mathrm{\theta }=\frac{m{v}^2}{R}$

$v=\sqrt{gR\mathrm{ }\cos \mathrm{\theta }}\mathrm{ }\mathrm{o}\mathrm{r}\mathrm{ }\cos \mathrm{\theta }=\frac{v^2}{gR}\mathrm{ }$.....(i)

From energy conservation

$\frac{1}{2}m\left[v^2-\frac{gR}{4}\right]=mgR\left(1-\mathrm{ }\cos \mathrm{\theta }\right)$

$\Rightarrow \frac{v^2}{2}-\mathrm{ }\frac{gR}{8}=gR-gR\mathrm{ }\cos \mathrm{\theta }$...(ii)

From (i) and (ii)$\mathrm{cos\theta }=\left(\frac{3}{5}\right)=0.6$