$[1/2$ Points$]$

SERPSE$1022\mathrm{.}3\mathrm{.}0$P$\mathrm{.}009.$

$($a$)$ A physics lab instructor is working on a new demonstration. She attaches two identical metal spheres with mass $m=0\mathrm{.}190g$ to strings of length $L$ as shown in the figure.

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Both spheres have the same charge of $8\mathrm{.}00$ nC $,$ and are in static equilibrium when $=4\mathrm{.}75.$ What is $L($in m $)?$ Assume the strings are massless.

$$ m

$($b$)$ What If$?$ The charge on both spheres is increased until each string makes an angle of $=9\mathrm{.}50$ with the vertical. If both spheres have the same electric charge, what is the charge $($in $nC)$ on each sphere in this case?

Use the same reasoning as in part $($a$),$ only now, use the length found in part $($a$)$ and the new angle to solve for the charge. nC