The end of a pencil of mass m and length L rests in a corner as the pencil makes an angl...

The end of a pencil of mass m and length L rests in a corner as the pencil makes an angle with the horizontal (x) direction (Fig. P8.82). If the pencil is released, it will rotate about point O with an acceleration Suppose the length of the pencil is increased by a factor of two but its mass is kept the same; the pencil would then have an angular acceleration when released. Find the ratio