Question

Find the acceleration of block of mass $m$ along the inclined plane $\left(a_x\right)$ if the acceleration of wedge, $b=4{\text{m/s}}^2$. All accelerations are w.r.t. to the ground and assume that the surface and pulley are smooth and the string is inextensible.

• A. $2{\text{m/s}}^2$
• B. $3{\text{m/s}}^2$
• C. $4{\text{m/s}}^2$
• D. $1{\text{m/s}}^2$

Answer 1

The correct option is A $2{\text{m/s}}^2$

The given system can be reframed as shown

From constrained condition and using intercept method we have,
${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2=0$
$\to a_x+b\cos \theta -b=0$
$\Rightarrow a_x=b(1-\cos \theta )=b(1-\cos {60}^{\circ })$
$a_x=4(1-\frac{1}{2})=2{\text{m/s}}^2$