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A heavy body of mass 25kg is to be dragg...

A heavy body of mass `25kg` is to be dragged along a horizontal plane (`mu` = `(1)/(sqrt(3))`. The least force required is `(1 kgf = 9.8 N)`

Text Solution

Verified by Experts

The correct Answer is:
12.5
Let the body is acted upon by a force at an angle with horizontal.
FBD:

`F cos theta = mu (mg - F sin theta) implies F = (mu mg)/(cos theta + mu sin theta)`. For min force, `(cos theta + mu sin theta)` should be max.
`implies (d)/(d theta) (cos theta + mu sin theta) = 0 implies - sin theta + mu cos theta = 0 implies tan theta = nu`. or
`theta = tan^(-1) (1//sqrt(3)) = 30^(@)`
Substituting this `theta` in expression of force we get `F_("min") = 12.5 kg` f.
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