Question

Find the acceleration of the system shown in the figure.

• A. $\frac{g}{7}$
• B. $\frac{g}{3}$
• C. $\frac{2g}{5}$
• D. $\frac{2g}{7}$

Answer 1

The correct option is D $\frac{2g}{7}$

Let us first draw the free body diagrams of $20kg$, $5kg$ and $10kg$ block.

From condition of equilibrium, we have
$20\text{g}-T_1=20a$...............(i)
And,
$T_1-T_2=5a$..................(ii)
On adding (i) & (ii), we have
$20g-T_2=25a$...........(iii)
Also, we have
$T_2-10g=10a$.........(iv)
On adding (iii) & (iv) we have
$20g-10g=35a⟹a=\frac{10g}{35}=\frac{2g}{7}$

Alternate:
Let us consider all three bodies as a system.
As the force on the left side is more (i.e. $20g>10g$) so, the system will move in the left direction.




From the figure, acceleration of the system will be
$a=\frac{\text{Effective force}}{\text{Total mass}}$
$⟹a=\frac{(20g-10g)}{35}=\frac{10g}{35}=\frac{2g}{7}$