JEE Advanced Model Paper 1 with solutions for online practice

Consider a strip on gate of dam at a depth of y from free surface of water ofwidth dy. Pressure force acting on this strip is, dF = (P0 + ρgy) dA - P0dA
= ρgy × ady
Total force , F = ∫ df =

h

∫

0

ρgya dy
F =

ρga×h2

2

Torque about 0 due to force on elemental strip is, dτ = dF × (h - y)
⇒ dτ = ρgay dy × (h - y)
Total torque τ = ∫ dτ =

h

∫

0

ρga × y (h - y) dy =

ρga×h3

6

If the point of application of force Fis at H above 0, then it produce the sametorque as found.
So F × H = τ ⇒ H =

h

3