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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 cms1. If g=10 ms2, 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 52 ms1.
Area of piston,
A=πD24 ,DDiameter of piston

Area of nozzle,
a=πd24 ,dDiameter 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 ms1 [Remain unchanged]

Vertical velocity at t=0.5 s,

vy=0+ayt

vy=gT=10×0.5=5 ms1

Further, net speed with which water hits the ground,

v=52+52=52 m/s

Option (D) is correct.

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