Question

Find the acceleration of the block of mass M in the situation shown in figure. All the surfaces are frictionless and the pulleys and the strings are light.

• A. $\frac{g}{3}$ up the plane
• B. $\frac{2g}{3}$ up the plane
• C. $\frac{g}{3}$ down the plane
• D. $\frac{2g}{3}$ down the plane

Answer 1

The correct option is A $\frac{g}{3}$ up the plane

Let the tension in the string be $T$.

From the FBD of body along incline:

$T-Mgsin{30}^{\circ }=Ma$

From FBD of body hanging:

$\left(2M\right)g-2T=\left(2M\right)a$

$⟹a=\frac{g}{3}$ up the plane.