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A solid sphere of radius $r$, made of material with density $\rho_s$, is moving through the atmosphere at constant pressure $p$ with velocity $v$. The net force only due to atmospheric pressure $F_p$ acting on the sphere at any time $t$ is

1. $\pi r^2 p$
2. $4\pi r^2 p$
3. $\frac{4}{3}\pi r^3 \rho_s \frac{dv}{dt}$
4. zero

Correct answer: zero

Solution

If the atmospheric pressure is constant everywhere, the pressure on all parts of the sphere is the same. The vector sum of pressure forces over a closed surface is zero because the forces cancel by symmetry.

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