The figure shows an incomplete schematic of a conventional

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The figure shows an incomplete schematic of a conventional lathe to be used for cutting threads with different pitches. The speed gear box U_s is shown and the feed gear box U_s is to be placed. P, Q, R and S denote locations and have no other significance. Changes in U_v should NOT affect the pitch of the thread being cut and changes in U_s should NOT affect the cutting speed.

The correct connections and the correct placement of Us are given by

1. Q and E are connected. U_s is placed between P and Q.
2. S and E are connected, U_s is placed between R and S.
3. Q and E are connected. U_s is placed between Q and E.
4. S and E are connected. U_s ' is placed between S and E

Correct Option: C

Taking the engineering of a conventional lathe, U_v is the back gear arrangement and U_s is the feed gear box (a) and (b) are then completely wrong.
Now if (c) is true then, if gear ratio of U_v is changed the relative velocity of spindle with respect to lead source in changed and hence pitch is changed.