Question

A pump of $200W$ power is lifting $2kg$ water per second from an average depth of $10m$. The velocity with which water comes out of the pump is :

$\left(g=9.8m{s}^{-2}\right)$ .

• A. $2m{s}^{-1}$
• B. $2.5m{s}^{-1}$
• C. $4m{s}^1$
• D. $3m{s}^1$

Answer 1

The correct option is A $2m{s}^{-1}$

Given,

$P=200W$

$m=2kg$

$h=10m$

$g=9.8m/s^2$

$v=?$ velocity of water with which water comes out of the pump.

The total energy, $T=mgh+\frac{1}{2}m{v}^2$

Power, $P=\frac{T}{time}$

$200=\frac{T}{1}$

$200=mgh+\frac{1}{2}m{v}^2$

$200=2\times 10\times 9.8+\frac{1}{2}\times 2\times v^2$

$4=v^2$

$v=\sqrt{4}m/s$

$v=2m/s$

The correct option is A.