b
\(\frac{G M}{x^{2}}=\frac{G(16 M)}{(10 a-x)^{2}}\)

\(\frac{1}{x}=\frac{4}{(10 a-x)} \quad \Rightarrow 4 x=10 a-x\)

\(x=2 a\) \(....(i)\)

\(COME\)

\(-\frac{ GMm }{8 a }-\frac{ G (16 M ) m }{2 a }+ KE\)

\(=-\frac{ GMm }{2 a }-\frac{ G (16 M ) m }{8 a }\)

\(KE = GMm \left[\frac{1}{8 a }+\frac{16}{2 a }-\frac{1}{2 a }-\frac{16}{8 a }\right]\)

\(KE = GMm \left[\frac{1+64-4-16}{8 a }\right]\)

\(\frac{1}{2} mv ^{2}= GMm \left[\frac{45}{8 a }\right]\)

\(V =\sqrt{\frac{90 GM }{8 a }}\)

\(V =\frac{3}{2} \sqrt{\frac{5 GM }{ a }}\)