Question

Find the acceleration of block of mass $m$ w.r.t ground if acceleration of $M$ is $b=4m/s^2$. (Assume all surfaces to be smooth and string inextensible.)

• A. $2m/s^2$
• B. $3m/s^2$
• C. $4m/s^2$
• D. $1m/s^2$

Answer 1

The correct option is C $4m/s^2$

The given system can be reframed as shown

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

From wedge constraint, the accelerations of the bodies along the perpendicular to the surface of contact should be equal.
$\Rightarrow a_y=b\sin \theta =b\sin {60}^{\circ }=\frac{\sqrt{3}}{2}\times 4=2\sqrt{3}{\text{m/s}}^2$
$\therefore a=\sqrt{a_x^2+a_y^2}=\sqrt{2^2+(2\sqrt{3}{)}^2}=\sqrt{16}=4{\text{m/s}}^2$
Thus, the net acceleration of the mass $m$ is $4m/s^2$