A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an i…

A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^\circ\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio\({v}_{1}^{2}:{v}_{2}^{2}\) is

[JEE Main 2025, 23 Jan (Shift 1)]