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Grade upto college level Mechanics

A cylindrical drum, pushed along by a board from an initial position shown in Fig. rolls forward on the ground a distance L/2, equal to half the length of the board. There is no slipping at any contact. Where is the board then? How far has the man walked?
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

Profile image of Shane Macguire
11 Years agoGrade upto college level
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1 Answer

Profile image of Deepak Patra
11 Years ago
The figure below shows the cylindrical drum moved by the man with a board of length L.
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233-2099_1.PNG