Q87 / 91 · KVPY 2020 (SB/SX) · Physics

A bottle has a thin nozzle on top. It is filled with water, held horizontally at a height of 1 m and squeezed slowly by hands so that the water jet coming out of the nozzle hits the ground at a distance of 2 m. If the area over which the handss s sare which the hands squeeze it is 10 cm2, the force applied by hands is close to (take g=10 m/s2 and density of water =1000 kg/m3)

Figure

  • A
    20 N
  • Correct answer
    B
    10 N
  • C
    5 N
  • D
    2.5 N

Solution

Figure

Apply Bernoulli between point- 1 and point-2.

P1+12ρV12=P2+12ρV22

P1=Patm + Force by hand  Area 

V1 tends to zero becomes area of point- 2 is very small.

P2=Patm

Patm +F/A=Patm +1/2ρV22⇒V22=2FPA …i

From Kinematics.

2=2( h)g×V2

∴V22=20 …ii

Using (i) and (ii) we get

20=2FρA ∴F=10 N

Hence, the correct answer is option: 'B'.

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