Explanation
Force on particle along the cord = $$mg\cos { \theta }$$
Distance travelled by the particle =$$\quad \dfrac { d }{ \cos { \theta } }$$, where $$d$$ is the diameter or the vertical circle.
$$s = \dfrac { a{ t }^{ 2 } }{ 2 }$$
$$\Rightarrow\ t =\sqrt { \dfrac { 2s }{ a } }$$.
Hence,$$\ t$$ is independent of $$\theta$$.
$$a= g\cos{\theta}\\AB = 2R\cos{\theta}\Rightarrow v^2 =u^2 + 2as \\v^2 = 0 + 2 (g\cos{\theta}) 2R\cos{\theta}\Rightarrow v^2 = 4gR \cos ^{2 }{\theta}\\ \Rightarrow v = 2\sqrt{ gR} \cos{\theta}$$
Using the relation for the radius (r) of loop.
$$\displaystyle \tan { \theta } =\frac { { v }^{ 2 } }{ rg } $$
or, $$\displaystyle \tan { { 12 }^{ o } } =\frac { { \left( 150 \right) }^{ 2 } }{ r\times 10 } $$
or, $$\displaystyle r=\frac { 2250 }{ 0.2125 } =10.6\times { 10 }^{ 3 }m=10.6\quad km$$
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