Question

What force should be applied on the wedge so that block over it does not move? (All surfaces are smooth).

• A. $F=\left(M+m\right)g\cot \theta$
• B. $F=\left(M+m\right)g\tan \theta$
• C. $F=\left(M+m\right)g\sin \theta$
• D. $F=\left(M+m\right)g\cos \theta$

Answer 1

Answer: (B)

$F=\left(M+m\right)g\tan \theta$

$\begin{array}{c}a=\left(\frac{F}{m+M}\right).....\left(1\right)\\ ma\cos \theta =mg\sin \theta \\ a=g\tan \theta \end{array}$
Put in $\left(1\right)$
$F=\left(M+m\right)gtan\theta$