    Question

# A syringe containing water is held horizontally with its nozzle at a height h=1.25 m above the ground as shown in the figure. The diameter of the piston is 5 times as that of the nozzle. The piston is pushed at a constant speed of 20 cms−1. If g=10 ms−2, then - A
The speed of water emerging from the nozzle is 5 ms1.
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B
The time taken by water to hit the ground is 0.5 s.
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C
The horizontal range, R=2.5 m.
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D
The magnitude of velocity with which the water hits the ground is 52 ms1.
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Solution

## The correct option is D The magnitude of velocity with which the water hits the ground is 5√2 ms−1.Area of piston, A=πD24 ,D→Diameter of piston Area of nozzle, a=πd24 ,d→Diameter of nozzle Using equation of continuity, AV=au ⇒u=AVa=D2d2×V=52×0.2=5 m/s Option (A) is correct. Time of flight, T=√2hg=√2×1.2510=0.5 s Option (B) is correct. Range, R=uT=5×0.5=2.5 m Option (C) is correct. Horizontal velocity, vx=5 ms−1 [Remain unchanged] Vertical velocity at t=0.5 s, vy=0+ayt ⇒vy=gT=10×0.5=5 ms−1 Further, net speed with which water hits the ground, v=√52+52=5√2 m/s Option (D) is correct.  Suggest Corrections  0      Explore more