Question

The value of F for which block of mass ${}^{\prime }{m}^{\prime }$ remains stationary with respect to wedge is?

• A. $F=\frac{(M+m)}{Tan\theta }\times g$
• B. $F=(m+M)gTan\theta$
• C. $F=\frac{Tan\theta }{(M+m)g}$
• D. None of these

Answer 1

The correct option is B $F=(m+M)gTan\theta$

$\begin{array}{c}a=\frac{F}{M+m}\\ \sum F_y=0\Rightarrow N\cos \theta =mg\\ \sum F_x=0\Rightarrow N\sin \theta =ma\\ a=g\tan \theta \\ F=a\left(M+m\right)\\ =g\tan \theta \left(M+m\right)\\ =F=\left(m+M\right)g\tan \theta \end{array}$

Hence,

option $\left(B\right)$ is correct answer.