Question

Find the net force acting on pulley $2$ assuming all strings and pulleys to be of negligible mass and all surfaces to be frictionless. $g=10{\text{m/s}}^2$.

• A. $45\text{N}$
• B. $90\text{N}$
• C. $45\sqrt{2}$
• D. $90\sqrt{2}$

Answer 1

The correct option is C $45\sqrt{2}$

Downward force on $5\text{Kg}=5\text{g}$
Downward force on $6\text{Kg}=3\text{g}$ as from FBD of $6Kg$ mass we have

$\therefore$ Acceleration of the system is given by,
$a=\frac{\text{Supporting Force}-\text{Opposing Force}}{\text{Total mass}}$
$=\frac{5g-6gsin{30}^{\circ }}{20}$
$=\frac{5\text{g}-3\text{g}}{20}=\frac{2g}{20}=1{\text{m/s}}^2$
From the FBD of $5Kg$ body, we have
$5g-T_1=5a⟹T_1=5(g-a)=45\text{N}$
Again, from FBD of pulley (2), we have

$F_{net}=\sqrt{T_1^2+T_1^2}=T_1\sqrt{2}=45\sqrt{2}\text{N}$