Question

All surfaces are smooth in following figure. Find $F$, such that block remains stationary with respect to wedge.

• A. $F=(M+m)gcot\theta$
• B. $F=Mgtan\theta$
• C. $F=(M+m)gtan\theta$
• D. $F=Mgcot\theta$

Answer 1

The correct option is C $F=(M+m)gtan\theta$

$a=$ acceleration of (wedge+block) in horizontal direction
$a=\frac{F}{M+m}.$
Now, analyzing the block w.r.t. wedge which is a non-inertial frame of reference we'll apply pseudo force towards left to block.

Since the block is stationary w.r.t. the wedge, the forces along the incline should cancel out.
Now, writing equation of motion along the incline
$macos\theta =mgsin\theta$
$a=gtan\theta$
$F=(M+m)gtan\theta$