Question

In the figure shown, all pulleys are massless and the strings are light. What is the acceleration of the block $m$ of mass $10kg$? (All surfaces are smooth and take $g=10m/s^2$.)

• A. $4.5{\text{m/s}}^2$ down the plane
• B. $4.5{\text{m/s}}^2$ up the plane
• C. $5{\text{m/s}}^2$ down the plane
• D. $5{\text{m/s}}^2$ up the plane

Answer 1

The correct option is A $4.5{\text{m/s}}^2$ down the plane

The given system can be framed as shown

FBDs of the pulleys and the blocks are as shown. Let $T$ be the tension in the string connected to pulley $P_7$.

Let $a$ be the acceleration of block $m$.

For $P_7:80-2T=m{a}_7\Rightarrow T=40\text{N}$ as $m=0$
For the block: The acceleration of the block $a$ is given as
$10g\sin 30°-\frac{40}{8}=10a$
$10\times 10\times \frac{1}{2}-5=10a$
$a=4.5{\text{m/s}}^2$ down the plane