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An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is
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Verified Answer
The correct answer is:
$m v^2$
$m v^2$
As power $\mathrm{P}=F . v .=\frac{F \ell}{t}$
$$
\begin{aligned}
& \text { or, } v\left(M \frac{v}{t}\right)=\frac{F . \ell}{t} \\
& \Rightarrow \quad M v^2=F \ell \ell \\
& \Rightarrow \quad F=\frac{M}{\ell} v^2=m v^2 \\
& {\left[\because \frac{M}{\ell}=m(\text { given })\right]}
\end{aligned}
$$
$$
\begin{aligned}
& \text { or, } v\left(M \frac{v}{t}\right)=\frac{F . \ell}{t} \\
& \Rightarrow \quad M v^2=F \ell \ell \\
& \Rightarrow \quad F=\frac{M}{\ell} v^2=m v^2 \\
& {\left[\because \frac{M}{\ell}=m(\text { given })\right]}
\end{aligned}
$$
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