d
(d) In order to complete a full circle, the normal force when the block is at the highest point of circular ramp should be greater than zero,

\(\mathrm{SO}\)

if value of point \(B=v_{B}\) Then,

At point \(B, m g+N=\frac{m v_{B}^{2}}{R}\)

\(\mathrm{AS} N>0\)

\(\Rightarrow v_{B}^{2}>m g R\)

At point \(-A\)

\(\frac{m v_{A}^{2}}{2}-\frac{m v_{B}^{2}}{2}=m g(2 R)[A s \Delta K E=-\Delta P E]\)

\(\frac{m v_{A}^{2}}{2}=2 m g R+\frac{m v_{B}^{2}}{2}\)

As \(v_{B}^{2}>m g R\)

\(\Rightarrow \frac{m v_{A}^{2}}{2}>2 m g R+\frac{m g R}{2} \Rightarrow \frac{m v_{A}^{2}}{2}>\frac{5 m g R}{2}\)

Also, \(\frac{m v_{A}^{2}}{2}-0=m g h\)

\(\mathrm{As}, m v_{A}^{2}>5 m g R \Rightarrow m g h>\frac{5 m g R}{2}\)

\(\Rightarrow h>5 r/ 2\)