Area of muzzle is A. Due to ejection of water (density $= ρ$ ) at a velocity v , the spring is compressed as shown in figure. The compression in spring, in equilibrium, is-

Question

Area of muzzle is A. Due to ejection of water (density = ρ ) at a velocity v , the spring is compressed as shown in figure. The compression in spring, in equilibrium, is-

TestHub · Accepted Answer

The force exerted by the ejected water is given by the rate of change of momentum.

Mass flow rate $= ρ A v$ .

Force $F = \frac{d p}{d t} = \frac{d ( m v )}{d t} = v \frac{d m}{d t} = v (ρ A v) = ρ A v^{2}$ .

In equilibrium, this force equals the spring force: $F = K x$ .

So, $K x = ρ A v^{2}$ .

Therefore, the compression $x = \frac{ρ A v ^{2}}{K}$ .

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