A small block of mass \( M \) is attached to a string of length \( L \) and is whirled in a horizontal circle at a constant speed \( v \) on a frictionless tabletop. The tension in the string is measured to be \( T \). The student then increases the speed of the block to \( 2v \). To keep the tension in the string equal to its original value \( T \), the student must adjust the length of the string. How should the length of the string be changed?