Consider the situation shown in the figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

The correct option is D $\frac{g}{10}$
Let ${\theta }_1,{\theta }_2$ be the angles of inclination of the blocks on the left and right side of the figure respectively.

Hence, ${\theta }_1=ta{n}^{-1}\frac{4}{3}={53}^{\circ }$

${\theta }_2=ta{n}^{-1}\frac{3}{4}={37}^{\circ }$

Let the acceleration of the blocks be towards left along the inclined planes.

From the FBD of the two blocks,

$ma=mgsin{\theta }_1-T$ and $ma=T-mgsin{\theta }_2$

$⟹a=\frac{g}{10}$