91Ó°ÊÓ

The force a charge exerts on another point is independent of the existence of other charges, according to the principle of superposition, and the net force a charge experiences as a result of the number of other charges acting on it is the vector sum of those forces.

Mass of both marbles are$\mathrm{m}=75.0\text{ g}=0.075\text{ k²µ}$

The diameter of marbles is $\mathrm{d}=2.00\text{ c³¾}=0.02\text{″¾}$

Wide container. So, $\mathrm{L}=32.00\text{ c³¾}$

(a)

At this point$\mathrm{A}$and $\mathrm{C}$, the forces have the same magnitude even if they are in the opposite direction

So, ${\mathrm{F}}_{\mathrm{A}}={\mathrm{F}}_{\mathrm{C}}$

At the center of the bottom marble $\mathrm{P}$, the summation of torque is zero.

So,

$\begin{array}{c}∑{\mathrm{Ï„}}_{\mathrm{P}}=0\\ {\mathrm{F}}_{\mathrm{A}}\left(\mathrm{³¦´Ç²õθ}\right)+{\mathrm{F}}_{\mathrm{C}}\left(\mathrm{³¦´Ç²õθ}\right)−\mathrm{W}=0\\ {\mathrm{F}}_{\mathrm{C}}\left(2\mathrm{³¦´Ç²õθ}\right)−\mathrm{W}=0\end{array}$

${\mathrm{F}}_{\mathrm{C}}=\frac{\mathrm{mg}}{2\cos 30°}$ (1)

Now, put numerical values in equation (1), we get

$\begin{array}{c}{\mathrm{F}}_{\mathrm{C}}=\frac{\left(0.0075\text{ k²µ}\right)\left(9.8{\text{″¾/s}}^2\right)}{2\cos 30°}\\ =0.42\text{ N}\end{array}$

So, ${\mathrm{F}}_{\mathrm{A}}={\mathrm{F}}_{\mathrm{C}}=0.42\text{ N}$

Now, at point $\mathrm{B}$, the exerted force is vertically due to the weight of the two marbles, so, it is given by

$\begin{array}{c}{\mathrm{F}}_{\mathrm{B}}=2\mathrm{W}\\ =2(0.0075\text{ k²µ})(9.8{\text{″¾/s}}^2)\\ =1.47\text{ N}\end{array}$

So, ${\mathrm{F}}_{\mathrm{B}}=1.47\text{ N}$

Hence, ${\mathrm{F}}_{\mathrm{A}}={\mathrm{F}}_{\mathrm{C}}=0.42\text{ N}$ and ${\mathrm{F}}_{\mathrm{B}}=1.47\text{ N}$

(b)

Each marble exerts a normal forceon the other and this normal force makes an angle $\mathrm{θ}=30°$with the vertical axis.

So, the normal force in relation to horizontal force${\mathrm{F}}_{\mathrm{A}}$could be given by

Hence, the force that each marble exerts on the other is $0.84\text{ N}$.