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)`

Options

A. 25 kg f
B. 2.5 kg f
C. 12.5 kg f
D. `25//sqrt(3)kg f`

Answer

C

Explanation

Let the body is acted upon by a force at an angle `theta` with horizontal
FBD

` F cos theta=mu (mg-F sin theta)`
`rArr F-(mumg)/(cos theta+mu sin theta)`. For min . Force, `(cos theta+musin theta)` should be max.
`rArr - sin theta+mu cos theta=0 rArr tan theta=mu` or ` theta=tan^(-1)(1//sqrt(3))=30^(@)` Subtituting `F_("min")=12.5 kg f`