Question

All surfaces are smooth in the adjoining figure. Mass of the wedge is $M$ and the mass of the block is $m$. Find $F$ such that block remains stationary with respect to wedge.

• A. $(M-m)gtan\theta$
• B. $(M+m)gtan\theta$
• C. $mgtan\theta$
• D. $Mgtan\theta$

Answer 1

The correct option is B $(M+m)gtan\theta$

Acceleration of (block + wedge) is a = $\frac{F}{(M+m)}$

Let us solve the problem by using both frames.

From inertial frame of reference (Ground)

F.B.D. of block w.r.t. ground (Apply real forces):

With respect to ground block is moving with an acceleration 'a'

$\therefore \sum F_y=0\Rightarrow Ncos\theta =mg$ .......... (i)

and $\sum F_x=ma\Rightarrow Nsin\theta =ma$ ........ (ii)

From Eqs. (i) and (ii)

a = g tan $\theta$

$\therefore F=(M+m)a=(M+m)gtan\theta$