Question

The heart is pumping blood at $x\mathrm{kg}$ per unit time, with constant velocity $v$. The force needed is

• A. $xv$
• B. $v\frac{dx}{dt}$
• C. $x\frac{dv}{dt}$
• D. zero

Answer 1

The correct option is C

$x\frac{dv}{dt}$

Step 1: Given data

The velocity of blood pumped $=v$
The momentum of the blood $=p$

Step 2: explanation.

If an object has a mass of m and a velocity of v, the object's momentum is defined as the mass multiplied by the velocity. m.v, The momentum is a vector quantity since it has both magnitude and direction.
Mass of blood pumped per unit time $\frac{\Delta m}{\Delta t}=x\mathrm{kg}$
Force is the rate of change of momentum, $F=\frac{\Delta p}{\Delta t}$, where$\Delta p=$$\Delta mv.$
Therefore, $F=\frac{\Delta mv}{\Delta t}$= $\frac{m\Delta v}{\Delta t}$.

Hence, option (c) is correct.