Question

In Guerickes experiment to show the effect of atmospheric pressure, two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $P$, then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is

• A. $2\pi R^{2}P$
• B. $4\pi R^{2}P$
• C. $\pi R^{2}P$
• D. $\pi R^{2}P/2$

Answer 1

The correct option is C $\pi R^{2}P$

Pressure inside the sphere is zero because of vacuum inside the sphere.
Net pressure acting on the sphere is atmospheric pressure from outside, so net force is only due to atmospheric pressure.
Resultant force of the atmospheric pressure acting on the hemisphere is equal to $P$ times the area of the hemisphere projected on the plane i.e. $\pi R^2$.
So net force required $F_{net}=P\times \pi R^2=\pi R^{2}P$