impringes normally on the plate with a velocity of 5m/s. Find the horizontal force applied at the centre of the gravity to maintain the plate in its vertical position. Find the corresponding velocity of the jet, if the plate id deflected through $30^{\circ}$ and the same force continues to act at the centre of gravity of the plate

Given w=58.86N, OG=10cm=0.1m d=2cm=0.02m

Distance of GGh=10cm=0.1m Velocity of jet v=5m/s

1.Horizontal Force, P at G to keep plate vertical

Normal; Force due to jet F=mv=(pAv)V

p$\frac{\pi}{4}d^{2}\times v^{2}$

$1000\times \frac{\pi}{4}\times (0.02)^{2}\times (5)^{2}$

=78.54 $\mu$

from fig, Taking moment about 'O'

$F\times OB=p\times h$

$78.54\times 0.15=p\times 0.1$

p=11.781 N

2) Velocity of jet , V if plate swings by $\Theta=30^{\circ}$ with same horizontal force p

Normal force due to jet $f_{1}=mv_{1}$=

=(P.A.$V_{1}.V_{1}$)

=$PAV^{2}_{1}$

=$1000\times \frac{\pi}{4}(0.002)^{2}\times v_{1}^{2}$

=31.416 $v_{1}^{2}$

p=11.781 N

Taking moment about hinge O we get

$w\times G.M+(P cos\Theta)OG_{1}=(f_{1}cos\Theta)\times OB_{1}$

But G,M-$OG_{1}\times Sin\Theta$

=$h sin\Theta$

=0.1sin30

=0.05 m

$OG_{1}=0.1m$

OB_{1}=\frac{OB}{cos\Theta}=\frac{0.15}{cos 30}=0.1732 m

on substituting values we get

$58.86\times 0.05+(11.781 cos30)0.1=(31.416 V_{1}^{2}cos 30\times 0.17312)$

$V_{1}$=0.917m/s