Question

All surfaces are smooth. Wedge is moving with acceleration a as shown. If block of mass m doesn't slide over wedge, then value of acceleration of wedge, a is : (g = 10 m/s²)

• A. 6 m/s²
• B. 13.33 m/s²
• C. 7.5 m/s²
• D. 8 m/s²

Answer 1

Answer: (B)

13.33 m/s²

Answer 2

For no sliding, the block must have zero acceleration component along the inclined plane. In the non‑inertial frame of the wedge, the block experiences:

• Gravitational acceleration: $g$ downward.
• Fictitious acceleration: $a$ acting opposite to the wedge’s acceleration (to the left).

Step 1. Resolve these accelerations along the plane (angle of incline $\theta = 53^\circ$). The component along the plane is given by:

$$(-a, -g) \cdot (\cos53^\circ,\sin53^\circ)= -a\cos53^\circ - g\sin53^\circ = 0.$$

Step 2. Solve for $a$:

$$a\cos53^\circ = g\sin53^\circ \quad\Longrightarrow\quad a = g \tan53^\circ.$$

Given $g = 10\,\text{m/s}^2$ and using $\tan53^\circ \approx 1.333$, we get:

$$a \approx 10 \times 1.333 = 13.33\,\text{m/s}^2.$$

Thus, the required acceleration of the wedge is 13.33 m/s².