Question

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

• A. $\frac{\rho v^{2}A}{2K}$
• B. $\frac{\rho v^{2}A}{K}$
• C. $\frac{2\rho v^{2}A}{K}$
• D. $\frac{4\rho v^{2}A}{K}$

Answer 1

The correct option is B $\frac{\rho v^{2}A}{K}$

Mass of liquid flowing $=\rho vA$
Momentum of liquid $=\rho v^{2}A$
going out in forward direction .
Momentum given to trolley in backward direction.
$=\rho v^{2}A\text{per sec.}$
= force on spring
$F=–Kx$
$\Rightarrow x=\frac{F}{K}$
Compression in spring $x=\frac{\rho v^{2}A}{K}$