Question

Two blocks of masses $10\text{kg}$ and $20\text{kg}$ are connected by a light string passing over a frictionless pulley as shown in the figure, the angle of inclination is ${30}^{\circ }$. If the system is released, the blocks move with an acceleration of

• A. $\frac{g}{2}m/s^2$
• B. $\frac{g}{4}m/s^2$
• C. $\frac{g}{6}m/s^2$
• D. $\frac{g}{8}m/s^2$

Answer 1

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

Using FBD of the masses

$T-10g\sin {30}^{\circ }=10a...\left(1\right)$
$20g-T=20a...\left(2\right)$
Solving (1) and (2) to get the value of acceleration $a$
$\Rightarrow 30a=20g-5g$
$a=\frac{15g}{30}=\frac{g}{2}{\text{m/s}}^2$