A gardener waters the plants by a pipe of radius 1 cm. The water comes out at rate of 10 cm3/s. The reactionary force exerted on the hand of gardener is
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11th
Physics
Laws of Motion
Newton's Third Law of Motion
A Gardner waters the plants...
PHYSICS
A Gardner waters the plants by a pipe of diameter 1 mm. The water comes out at the rate or 10 cm
3
/sec. The reaction force exerted on the hand of the Gardner is:
A
0 N
B
1.27×10
−2
N
C
1.27×10
−4
N
D
0.127 N
MEDIUM
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ANSWER
reaction force = Av
2
p
F=v
dt
dm
where vis the velocity of water
dt
dm
is the rate of mass flow
F=v
dt
dm
=vp
dt
dv
wherep is the density
A= area of cross section then F=vpA
dt
dv
=pAv
2
in this question directly
dt
dv
is given
dt
dv
=Av
10=
4
πd
2
v
therefore v=
πd
2
40
now F=
πd
2
40
p10 =
22×10
−2
400×1×7
= 127.27×10
−2
dyne
1dyne = 10
−5
N
now F=
10
−2
127.27
×10
−5
=0.127N
option is D
The accurate alternative is C. 7/22× 10⁻³N.
Given:
- Let the density of water be ρw, ρw = 1000kg/m³,
- Radius of the pipe, (r) = 1cm = 10⁻²m
Formulas used:
- Area of the cross-phase of the tube,
- A=πr²Volume,
- V = place of cross-phase × period of pipe,
- F = Δ(mv)/t, x=ΔV/t,
- Density (ρ)=Mass(m)Volume(V)
Explanation:
- A=πr² =22/7 ×(10⁻²)²m²,
- x=ΔV/t =10cm³/sec, F=ρ× x × x/A
- ⇒F = ρ.x²/A
- ⇒F = (10³×10⁻⁵)²/22/7× 10⁻³N= 7/22× 10⁻³N
- The reactionary pressure on the hand of a gardener=
- 7/22× 10⁻³N.
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