In a cylindrical grinding machine the longitudinal (axial) traverse of the workpiece past the grinding wheel is provided by the table with its sliding (reciprocating) mechanism. The workpiece, mounted between the headstock and tailstock centres, sits on this table, and as the table slides back and forth along the machine bed the whole length of the job is presented to the wheel — allowing a narrow wheel to grind a long cylinder.

Understanding the separate motions clarifies why the table is the right answer. Cylindrical grinding needs several independent movements working together:

• Grinding-wheel rotation — supplies the high cutting speed at the wheel periphery.
• Workpiece rotation — driven by the headstock spindle so the entire circumference is ground.
• Longitudinal feed — the table reciprocation that moves the job axially past the wheel (the motion asked about).
• Infeed (cross-feed) — the radial movement of the wheel head that controls depth of cut and final diameter.

The other options perform different roles and give no longitudinal motion. The spindle rotates the work about its own axis (a rotary, not a lengthwise, motion). The wheel guard is purely a safety cover shielding the operator from the fast-spinning wheel. The coolant system with pump only supplies cutting fluid to cool the grinding zone and flush away swarf. None of these traverses the workpiece along its length, so the table with sliding mechanism is correct.