Question

Two bodies of mass 4 $\text{kg}$ and 6 $\text{kg}$ are tied to the end of a massless string. The string passes over the pulley, which is frictionless (see figure). The acceleration of a system in terms of acceleration due to gravity$\left(g\right)$ is

• A. $\frac{g}{5}$
• B. $\frac{g}{10}$
• C. $g$
• D. None of the above

Answer 1

The correct option is A $\frac{g}{5}$

The force balancing equation for $4\text{kg}$ block is :
$T-4g=4a$

Simplify for $T$:

$T=4a+g$

On the other hand, the expression for $6\text{kg}$ block is:
$6g-T=6a$

Substitute the value of $T$ in above expression :

$6g-(4a+g)=6a$

$a=\frac{2g}{10}=\frac{g}{5}$
Therefore, acceleration will be $\frac{g}{5}$.