Question

An engine pumps a fluid of density $800kg/m^3$ through a tube of regular cross-sectional area of $5c{m}^2$ with a speed of $20cm/s.$ The rate at which kinetic energy is given to the fluid is

• A. $3.2\times {10}^{3}J/s$
• B. $1.6\times {10}^{-3}J/s$
• C. $1.6\times {10}^{3}J/s$
• D. $3.2\times {10}^{-3}J/s$

Answer 1

The correct option is B $1.6\times {10}^{-3}J/s$

Kinetic energy, K.E. $=\frac{1}{2}m{v}^{2}Density,\rho =\frac{mass}{vlume}=\frac{m}{v}\Rightarrow m=\rho V\text{Density,}\rho =800kg/m^3\text{Cross-sectional area, A}=5c{m}^2=5\times {10}^{–4}{m}^{2}Speed,v=20cm/s=0.2m/s$
Volume of the fluid ejected in t s through the tube, V = Avt
Rate at which kinetic energy is given to the fluid $=\frac{\frac{1}{2}m{v}^2}{t}=\frac{\frac{1}{2}\times \rho \times V\times v^2}{t}(\because V=Avt)=\frac{1}{2}\times \rho \times A\times v^3=\frac{1}{2}\times 800\times 5\times {10}^{-4}\times (02{)}^3=16\times {10}^{-4}J/s=1.6\times {10}^{-3}J/s$
Hence, the correct answer is option (b).