Question

In the given figure, All surface are smooth & $g=10m/s^2$. The force F required to keep 4 kg in equilibria is (Write upto two digits after the decimal point)

Answer 1

Free body diagram of the top block is,
$N_{24}\cos 53=20\Rightarrow N_{24}=\frac{100}{3}$

Free body diagram of the middle block is,

$N_{34}\cos 37=N_{24}\cos 53+m_{4}g$
$N_{34}\times \frac{4}{5}=\frac{100}{3}\times \frac{3}{5}+40\Rightarrow N_{34}=75N$
$\therefore F=N_{34}\sin 37+N_{24}\sin 53=71.67N$