A student investigates three ideal hand-cranked pencil sharpeners, \(X\), \(Y\), and \(Z\), that use gear systems to rotate identical cylindrical cutting blades. To completely sharpen an unsharpened pencil, the cutting blades must rotate through a fixed total angle \(\Delta \theta_{\text{blade}}\) against a constant resistive torque \(\tau_0\) caused by wood resistance and internal friction. The gear ratio is defined as \(g = \dfrac{\omega_{\text{blade}}}{\omega_{\text{crank}}}\), with values \(g_X = 1\), \(g_Y = 2\), and \(g_Z = 4\). If the student uses each sharpener to completely sharpen an identical pencil by turning the crank handle at the same constant angular velocity, which of the following correctly compares the total work \(W\) done by the student on the crank handle and provides a correct justification?