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GATE 2019 CE (CE2) – Question 22

Fluid Mechanics · Properties of fluids, fluid statics · 1 mark · Multiple choice

A solid sphere of radius r and material density $\rho_s$ moves through an atmosphere of constant pressure p with velocity v. Find the net force due ONLY to atmospheric pressure at time t.

  1. $\pi r^2p$
  2. $4\pi r^2p$
  3. $\frac43\pi r^3\rho_s\frac{dv}{dt}$
  4. zero

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Correct answer: (D) zero

Explanation

Constant pressure acts inward normal over a closed surface. Its net force is $-p\iint_S\hat n\,dA=0$, because the integral of the surface normal is zero. Answer **D**. Atmospheric drag or spatially varying pressure is excluded.