Answer:
Explanation:
First we need to find the capacitance of the capacitor.
The capacitance is given by:
Where 
is the air permittivity, which is approximately 8.85 * 10^(-12)
The radius is 12/2 = 6 mm = 0.006 m, so the area of the capacitor is:
So the capacitance is:
The time constant of a rc-circuit is given by:
So we have that:
1) Horizontal velocity, Vx
Vx is constant and equal to 5.0 m/s
The graph Vx(t) = 5.0 m/s is a horizontal line (parallel to the horizontal t-axis). that intercepts the vertical-axis at 5.0 and runs from t = 0 to t = 2.
2) Vertical velocity, Vy
Vy = gt = 10t
d = at^2 / 2 => tmax = √(2d / a) = √(2*20m/10m/s^2) = 2 s
Graph Vy is an inclined line with slope 10 m/s^2, that runs from t =0 to t = 2 s, and passes through the points (0,0), (1,10), and (2,20).
F1 = G * m*m / [2r] ^2 = G * m^2 / 4r^2
Given the the mass is proportional to the volume and the volume is proportional to r^3, the mass of each big sphere is 3^3 = 27 times the mass of the small spheres. And the distance between the centers is 3r + 3r = 6r
F2 = G * [27m * 27m]/* [6r]^2 = G* 27^2 m^2 / 36r^2 = 81 G*m^2 / 4r^2 = 81*F1
Therefore, F2 = 81F1
Answer: option D) 81F1.
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