# All surfaces are smooth in the figure. Find F such that block of mass m resting on a wedge of mass M remains stationary with respect to wedge

a) $(M-m) g \tan \theta$ b) $Mg \tan \theta$ c) $\frac{M}{m} g \tan \theta$ d) $(M+m) g \tan \theta$

Free body diagram of block of mass m
The block moves with acceleration a w.r.t ground
$a= \large\frac{F}{M+m}$
$\Sigma F_y=0=>N \cos \theta=mg$
$\Sigma F_x=0=>N \sin \theta=ma$
$a= g \tan \theta$
$F= a(M+m)$
$\quad=g \tan \theta(M+m)$
Hence d is the correct answer.
edited May 26, 2014