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Q.

Water (density ρ)is flowing through the uniform horizontal tube of cross-sectional area  A with a constant speed  v as shown in the figure. The magnitude of force exerted by the water on the curved corner of the tube is (neglect viscous forces)

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a

3ρAv2

b

2ρAv2

c

2ρAv2

d

ρAv22

answer is A.

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Detailed Solution

GivenDensity of water = ρCross-sectional area= AConstant speed= vAlong  x and  y directions along in momentum of water is P→i=mvj^Pf→=mv32i^-mv2j^∆P→=Pf→-Pi→=mv32i^-mv32j^⇒ΔP¯net=32mv2+-32mv2=3mvForce on bend is rate of change of momentum ⇒ΔF¯net=3dmdt.v=3ρAv2
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