Answer
$a)\space T=560N=130lb $ and No
$b) \space F_G = 4.5\times 10^{-34}$
Work Step by Step
$a)$
$n=$Total no. of protons in 1 gram of proton
$Q = $Total charge on 1 gram of proton
$e = $charge on one proton = $1.6\times 10^{-19}$
Since mass of one proton is $1.67\times 10^{-27}$
$\therefore n = {1\times 10^{-3} \over 1.67 \times 10^{-27}} = 5.988 \times 10^{23}$
$Q = ne = 5.988\times 10^{27} \times 1.6\times 10^{-19} = 95808C$
Also $r = 3.844\times 10^8$
$Tension(T) = F = {kq^2\over r^2}={9\times 10^9\times (95808)^2\over (3.844 \times 10^8)^2}=560N=130lb$
No, we don't have to consider gravitational Force since it's magnitude is way smaller the electrostatic force as both depends on $1\over r^2$ but the gravitational constant $G = 6.67\times 10^{-11}$ is way smaller than the constant $k = 9\times 10^9$
$b) $Gravitional Force $F_G = {Gm^2\over r^2} = {6.67\times 10^{-11}\times (1\times 10^{-3})^2\over (3.844\times 10^8)^2} = 4.5\times 10^{-34}$
