BITSAT 2015 Paper

The net force acting on the gate element of width dy at a depth y from the surface of the fluid, is
dy = (p0+ρgy−p0) × 1 dy
= ρgydy
Torque about the hinge is
dτ = pgydy × (

1

2

−y)
Net torque experienced by the gate is

τnet = ∫ dτ + F ×

1

2

=

1

∫

0

ρg ydy (

1

2

−y) + F ×

1

2

= 0
⇒ F =

ρg

6

i.e., The force F required to hold the gate stationary is

pg

6