Which of the following instruments measures the earth's gravitational pull on a body?

Step 1: Identify the region and apply Gauss's law. Since $r = 0.4\ m > R = 0.3\ \mathrm{m}$, the Gaussian surface is a sphere of radius $r$ enclosing the total charge $Q$.

Gauss's law:
$\oint \vec{E} \cdot d\vec{A} = \frac{Q_encl}{\epsilon_0}$

Step 2: For spherical symmetry, $E$ is constant on the Gaussian surface and perpendicular to it.
$E \cdot 4\pi r^2 = \frac{Q}{\epsilon_0}$

Step 3: Solve for $E$.
$E = \frac{Q}{4\pi \epsilon_0 r^2}$

Step 4: Substitute constants. Use $k = \frac{1}{4\pi \epsilon_0} = 9.0 \times 10^9\ \mathrm{N \cdot m^2 / C^2}$.
$E = k \frac{Q}{r^2}$

Step 5: Plug in values: $Q = 5.0 \times 10^{-9}\ \mathrm{C}$, $r = 0.4\ \mathrm{m}$.
$E = (9.0 \times 10^9) \frac{5.0 \times 10^{-9}}{(0.4)^2}$

Step 6: Simplify numerator and denominator.
$E = (9.0 \times 10^9)(5.0 \times 10^{-9}) \div 0.16$
$E = 45 \div 0.16$

Step 7: Compute the value.
$E = 281.25\ \mathrm{N/C}$

281 N/C