Curved surface of a vessel has shape of a truncated cone having semi vertex angle $37 °$ . Vessel is full of water (density $ρ = 1000 k g l m^{2}$ ) up to a height of 13 cm and is placed on a smooth horizontal plane. Upper surface is opened to atmosphere. A hole of $1.5 c m^{2}$ is made on curved wall at a height of 8cm from bottom in figure. Area of water surface in the vessel is large as compared to the area of hole.

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Initial velocity of efflux is $1 m / \sec$

Horizontal force required to keep the vessel in static equilibrium is 0.12N

Initial horizontal range of water jet from point B is 6.65 cm

Horizontal force required to keep the vessel in static equilibrium is 0.15N

answer is A, D.

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Detailed Solution

$= ρ v^{2} \cos 37^{0} = 0.12 N$ $v = \sqrt{2 g (Δ h)} = \sqrt{2 \times 10 \times (5 / 100)} = 1 m l s^{3}$
Range $= 0.8 \times \frac{1}{10} = 8 c m$
Range from $B = 8 c m - 8 c m \times \frac{3}{5} = 3.2 c m$
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$v \cos θ t - \frac{1}{2} g t^{2} = - 0.08 \Rightarrow 0.6 t - 5 t^{2} + 0.08 = 0 \Rightarrow t = 0.1 s$
Horizontal force required