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The figure shows a liquid being pushed out of a horizontal tube by a piston having an area of cross-section 2.0 cm², a force F driving the piston to the right and the liquid leaving through a narrow outlet at the far end. The area of cross-section at the outlet is 10 mm². If the piston is pushed at a speed of 4 cm s⁻¹, the speed of the outgoing fluid is ______ cm s⁻¹.

Asked in JEE Main 10th April 2nd Shift 2023 · Equation of continuity

Figure: Equation of continuity
Answer: 80

Step-by-step solution

Given: piston area A=2.0 cm²=200 mm², outlet area a=10 mm², piston speed v=4 cm s⁻¹.

The liquid is incompressible, so the volume swept out by the piston each second leaves through the outlet in the same second.

Av=av', so v'=vA/a.

A/a=(200)/(10)=20, so v'=4×20.

v'=80 cm s⁻¹.

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