Question

A heavy body of mass $25kg$ is to be dragged along a horizontal plane $\left(\mu =\frac{1}{\sqrt{3}}\right).$ The least force required is :-

• A. $25kgf$
• B. $2.5kgf$
• C. $12.5kgf$
• D. $6.25kgf$

Answer 1

Answer: (C)

Angle of friction $\theta ={\left(tan\right)}^{-1}(\mu )$
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 $Fcos\alpha =\mu N=\mu (mg-Fsin\alpha )$
$\therefore F=\frac{\mu mg}{cos\alpha +\mu sin\alpha }$
$F_{min}=\frac{\mu mg}{\sqrt{1+{\left(\mu \right)}^2}}=\frac{\left(\frac{1}{\sqrt{3}}\right)(25)(g)}{\sqrt{1+\frac{1}{3}}}$
$=12.5g$
$=12.5kgf$