A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3\, m / s\) (as shown in figure). Maximum height with respect to the initial position covered by it will be \(...........cm\).

Initial \(KE =\) Translational \(KE +\) Rotational \(KE\)

\(=\frac{1}{2} mv ^2+\frac{1}{2} I \omega^2\)

In case of rolling \(v = R \omega\)

\(=\frac{1}{2} m v^2+\frac{1}{2} \times \frac{2}{3} m R^2 \times \frac{v^2}{R^2}\)

\(=\frac{5}{6} m v^2\)

Apply energy conservation

\(KE _{ i }+ PE _{ i }= KE _{ f }+ PE _{ f }\)

\(\frac{5}{6} mv ^2= mgh\)

\(h =\frac{5}{6 \times 10} \times 9\,m =\frac{15}{20} m =75\,cm\)