Question

Find the acceleration of block of mass $m$ (in $m/s^2$) along the plane (w.r.t ground), if the acceleration of block of mass $M$ is $bm/s^2$. Assume the surface to be smooth and string inextensible.

• A. $b$
• B. $\frac{b}{2}$
• C. $\frac{3b}{2}$
• D. $2b$

Answer 1

The correct option is C $\frac{3b}{2}$

The given system can be reframed as shown
Let $a_p$ be the acceleration of the mass $m$ down the plane


From constrained condition and using intercept concept, we have
${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2+{\stackrel{..}{L}}_3+{\stackrel{..}{L}}_4=0$
$\Rightarrow -b+0-b+b\cos \theta +a_p=0$
$\Rightarrow a_p=2b-b\cos \theta$
As $\theta ={60}^{\circ }$
$\Rightarrow a_p=2b-\frac{b}{2}=\frac{3b}{2}$