NEET Power MCQs & PYQs

Practice NEET Power Questions

Question 11:

moderate

The heart of a man pumps $5\text{ litres}$ of blood through the arteries per minute at a pressure of $150\text{ mm}$ of mercury. If the density of mercury be $13.6 \times 10^3\text{ kg/m}^3$ and $g = 10\text{ m/s}^2$, then the power of heart in watt is:

(2015 Re)

Power is given by $P = p \left(\frac{dV}{dt}\right)$. Pressure $p = h\rho g = 0.15 \times 13.6 \times 10^3 \times 10 = 2.04 \times 10^4\text{ Pa}$. Volume flow rate $\frac{dV}{dt} = \frac{5 \times 10^{-3}}{60}\text{ m}^3\text{/s}$. Multiplying these gives $1.70\text{ W}$.

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Question 12:

moderate

A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to:

(2012 Mains)

From constant power $P_0 = mv\frac{dv}{dt}$, integrate both sides to get $v^2 = \frac{2P_0 t}{m}$. Thus, velocity $v \propto t^{1/2}$.

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Question 13:

moderate

A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, the power delivered to the particle is:

(2010 Mains)

Power delivered is the rate of change of kinetic energy: $P = \frac{\Delta K}{T} = \frac{\frac{1}{2}MV^2 - 0}{T} = \frac{1}{2}\frac{MV^2}{T}$.

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Question 14:

moderate

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\text{ m/s}$. The mass per length of water in the pipe is $100\text{ kg/m}$. What is the power of the engine?

(2010 Pre)

Mass flow rate is $\frac{dm}{dt} = \lambda v = 100 \times 2 = 200\text{ kg/s}$. Power of the engine equals the kinetic energy given to water per second: $P = \frac{1}{2}\left(\frac{dm}{dt}\right)v^2 = \frac{1}{2}(200)(2)^2 = 400\text{ W}$.

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Question 15:

moderate

How much water a pump of $2 \text{ kW}$ can raise in one minute to a height of $10 \text{ m}$? (Take $g = 10 \text{ m/s}^2$)

(1990)

Using $P = \frac{mgh}{t}$, mass $m = \frac{P \cdot t}{gh} = \frac{2000 \times 60}{10 \times 10} = 1200 \text{ kg}$, which equals $1200 \text{ litres}$.

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Question 16:

moderate

An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

(2009)

Mass flowing per second is $\frac{dm}{dt} = mv$. The rate of kinetic energy is $\frac{1}{2} \left(\frac{dm}{dt}\right) v^2 = \frac{1}{2} mv^3$.

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