Question

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move (Take $g=10m/s^2$)

• A. $20\text{N}$
• B. $10\text{N}$
• C. $12\text{N}$
• D. $15\text{N}$

Answer 1

The correct option is A $20\text{N}$

The given arrangement can be reframed as shown
From the FBD of the block we have
$N=mg+F_v=\sqrt{3}g+F\cos {30}^{\circ }$
$\Rightarrow N=(10\sqrt{3}+\frac{\sqrt{3}F}{2})\text{N}$
As we have to find out the maximum value of applied external force $F$, the friction force acting on the block will be limiting in that case.
$\therefore$ limiting friction will be given as
$f_{\text{max}}=\mu N=\left(\frac{1}{2\sqrt{3}}\right)(10\sqrt{3}+\frac{\sqrt{3}F}{2})$
$\Rightarrow f_{\text{max}}=5+\frac{F}{4}$

Now, from the equation of the force in the horizontal direction, we have
$F_H=f_{\text{max}}\Rightarrow F\sin {30}^{\circ }=5+\frac{F}{4}$
$\Rightarrow \frac{F}{2}=5+\frac{F}{4}\Rightarrow F=20\text{N}$