Question

A block of mass $2 \,kg$ slides down the face of a smooth $45^{\circ}$ wedge of mass $9 \,kg$ as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge

• A. $2\,m/s^{2}$
• B. $\frac{11}{\sqrt{2}} m /s^{2}$
• C. $1\,m/s^{2}$
• D. none of these

Answer 1

Answer: (C)

$a$ is accelerate of block w.r.t. wedge

For block:
$N+mA\,sin\,45^{\circ}$
$=mg\,cos\,45^{\circ} \ldots(i)$
For wedge: $N\,sin\,45^{\circ}=MA \ldots(ii)$
From (i) and (ii) $A = 1\,m/s^{2}$