KVPY 2019 SB SX Exam Previous Papers

Question : 98 of 120

Marks: +1, -0

Consider the configuration of a stationary water tank of cross section area

A_0

, and a small bucket as shown in figure.

What should be the speed, v, of the bucket so that the water leaking out of a hole of cross-sectional area A (as shown) from the water tank does not fall outside the bucket? Take h = 5m, H = 5m, g = 10 m/s

^{2}

,A = 5 cm

^{2}

and A

_0

= 500 cm

^{2}

1 m/s
0.5 m/s
0.1 m/s
0.05 m/s

Validate

Solution:

R = V_ e √{{ 2H}/g}

=√{2gh}√{{2H}/g}=2√{hH}

so velocity

V =-{dR}/{dt}=-2√H{d√h}/{dt}

V = - 2√H1/2√h{dh}/{dt}=-√{H/h}{dh}/{dt}

…….(1)
Now

AV_e

= Rate of flow of volume

A√{2gh}=A_0[{-dh}/{dt}]

…..(2)
from (1) and (2)

V=√{H/h}A/A_0β√{2gh}

=1/100√{2×10×5}=1/10

m/s

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