Question

A mass m is placed on a wedge (triangular block) of mass M. The wedge moves on a smooth horizontal surface. What should be the force F applied on the wedge to the right, so that m remains stationary with respect to wedge? (Ignore any friction)

• A. $g \tanθ$
• B. $mg\cosθ$
• C. $(M+m)g\tanθ$
• D. $(M+m)g\cosecθ$

Hint:

The acceleration of the wedge must be $g\tanθ$ for the block to not slide.

Answer 1

The Correct Option is C

Step 1: For m to remain stationary relative to wedge, acceleration of wedge = acceleration of m horizontally.

Step 2: For m: $N\sinθ = ma$, $N\cosθ = mg$. So $a = g\tanθ$.

Step 3: For system: $F = (M+m)a = (M+m)g\tanθ$.