KVPY 2019 SB SX Exam Previous Papers

Consider the wall of a dam to be straight with height H and length L. It holds a lake of water of height h(h < H) on one side. Let the density of water be ${\mathit{\rho }}_{\mathit{w}}$. Denote the torque about the axis along the bottom length of the wall by ${\mathit{\tau }}_1$. Denote also as similar torque due to the water up to height h/2 and wall length L/2 by ${\mathit{\tau }}_2$. Then $\frac{{\mathit{\tau }}_1}{{\mathit{\tau }}_2}$ (ignore atmospheric pressure) is