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GATE 2024 PI – Question 34

General Engineering · Theory of Machines and Design · 1 mark · Numerical answer

An offset slider–crank is shown, with crank l, connecting rod 3l and offset l. For l = 10 cm, find slider stroke (one decimal cm).

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Correct answer: 21.3 to 21.5

Explanation

At dead centers the crank and rod are collinear, with pivot-to-slider distances 4l and 2l. Their horizontal projections are $\sqrt{(4l)^2-l^2}=l\sqrt{15}$ and $\sqrt{(2l)^2-l^2}=l\sqrt3$. Stroke is $10(\sqrt{15}-\sqrt3)=21.4093$ cm, giving **21.4 cm**.

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