Question

The minimum value of F such that the block is at rest is $(\tan \theta >\mu )$

• A. $\frac{mg(\cos \theta -\mu \sin \theta )}{\sin \theta +\mu \cos \theta }$
• B. $\frac{mg(\cos \theta +\mu \sin \theta )}{\sin \theta -\mu \cos \theta }$
• C. $\frac{mg(\sin \theta +\mu \cos \theta )}{\cos \theta -\mu \sin \theta }$
• D. $\frac{mg(\sin \theta -\mu \cos \theta )}{\cos \theta +\mu \sin \theta }$

Answer 1

The correct option is C $\frac{mg(\sin \theta +\mu \cos \theta )}{\cos \theta -\mu \sin \theta }$

$\begin{array}{c}N=F\sin \theta +mg\cos \theta ....\left(1\right)\\ F\cos \theta =f+mg\sin \theta \\ =\mu \left[f\sin \theta +mg\cos \theta \right]+mg\sin \theta \\ =F\left[\cos \theta -\mu \sin \theta \right]\\ =mg\left[\mu \cos \theta +\sin \theta \right]\\ F=\frac{mg\left[\mu \cos \theta +\sin \theta \right]}{\cos \theta -\mu \sin \theta }\\ Hence,\\ optionCiscorrectanswer.\end{array}$