GATE 2024 PI – Question 56
A CNC tool travels anticlockwise from A = (0,0) to B = (10,10) on the shown quarter-circle centered at C = (0,10), all mm. P has X coordinate 6 mm. X feed at P is 6 mm/min. Find Y feed there (one decimal mm/min).
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Correct answer: 4.5 to 4.5
Explanation
Circle equation is $x^2+(y-10)^2=100$. At x = 6 on the lower branch, y = 2. Differentiate: $2x\dot x+2(y-10)\dot y=0$, giving $\dot y=-x\dot x/(y-10)=-6(6)/(-8)=\mathbf{4.5}$ mm/min.