Thank you for reporting, we will resolve it shortly
Q.
A heavy body of mass $25\,kg$ is to be dragged along a horizontal plane $\left(\mu = \frac{1}{\sqrt{3}}\right).$ The least force required is :-
NTA AbhyasNTA Abhyas 2022
Solution:
Angle of friction $\theta =\left(tan\right)^{- 1}\left(\right.\mu \left.\right)$
or $\theta =\left(tan\right)^{- 1}\left(\frac{1}{\sqrt{3}}\right)=30^\circ $
Suppose the body is dragged by a force $F$ acting at an angle $\alpha $ with horizontal. Then,
$N=mg-Fsin\alpha $
and $Fcosα=\mu N=\mu \left(\right.mg-Fsinα\left.\right)$
$\therefore F=\frac{μmg}{cosα + μsinα}$
$F_{m i n}=\frac{μmg}{\sqrt{1 + \left(\mu \right)^{2}}}=\frac{\left(\frac{1}{\sqrt{3}}\right) \left(\right. 25 \left.\right) \left(\right. g \left.\right)}{\sqrt{1 + \frac{1}{3}}}$
$=12.5\,g$
$=12.5\,kgf$
