Question

Find the minimum value of force $F$ for which the system remains at rest. Take $g=10m/s^2$.

• A. $60N$
• B. $72N$
• C. $80N$
• D. $90N$

Answer 1

The correct option is B $72N$

The FBDs of the system can be shown as:

The $4kg$ block will try to move towards right, so the frictional force $f$ will act on it towards left.

Thus, from the figure shown, we can write the equation of force as
$\left(a\right)T=8g$
$\left(b\right)T=F+f=F+\mu \left(4g\right)$
From the above two equations we get
$\Rightarrow 8g=F+0.2\times 4\times 10$
$\Rightarrow F=80-8=72N$