Assertion : Water is flowing through a horizontal tube, the static pressure and total pressure at any point are `1.20xx10^(5)` P and `1.28xx10^(5)` P . If the density of water is `1000 kg//m^(3)` , the velocity of liquid flow is 4 m/s.
Reason : Work done on the liquid by difference in pressure is equal to gain in K.E. of liquid

Options

A. both Assertion and Reason are true and the Reason in the correct explanation of the Assertion.
B. both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
C. Assertion is true but the Reason is false.
D. both Assertion and Reason are false.

Answer

A

Explanation

Difference of pressure,
`p = (1.28xx10^(5) - 1.20xx10^(5)) = 0.08xx10^(5)` Pa
If a is the area of cross-section of the tube and v is the velocity of liquid flowing through it, then volume liquid flowing per second through the tube = a v. Mass of liquid flowing per second through the tube = a v `rho`
Work done on the liquid by excess of pressure `=Pxx a v`
Gain in K.E. `=(1)/(2) (a v rho)v^(2)`
Hence, `p a v =(1)/(2) a v rhoxx v^(2)`
or `v= sqrt((2p)/(rho)) = sqrt((2xx0.08xx10^(5))/(1000)) =4m//s`
Hence, both Assertion and Reason are correct and Reason is the correct explanation of Assertion.