A square frame made up of a wire of mass `m` and length `l` is held in horizontal plane. It is free to rotate about `AD`. If the frame is released. What is the work done by gravity during the time frame rotates through an angle of `90^@`.
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Answer

`(mgl)/(8)`

Explanation

Total length of wire is 'l' and mass is `m` so each side length `= (l)/(4)` and mass `= (m)/(4)`.
Work done of gravity is calculate by the displacement of `COM` in vertical direction -
Work done by gravity `= (mg)/(4) (l)/(8) + (mg)/(4) (l)/(8) + (mg)/(4) (l)/(4)`
work done by gravity `= (mgl)/(8)`.