Question

A rectangular plate $2m\times 3m$ is immersed in water in such a way that its greatest and least depth are $6m$ and $4m$ respectively, from the water surface. The total thrust on the plate is

• A. $294\times 10^{3}N$
• B. 294 N
• C. $100\times 10^{3}N$
• D. $400\times 10^{3}N$

Answer 1

Answer: (A)

Given, size of the plate $=2m\times 5m$ and
Greatest and least depths of the plate are $6m$ and $4m$.
We know that area of the plate $A=2\times 3=6m^2$
and depth of centre of the plate
$x=\frac{6+4}{2}=5m$
$\therefore$ Total thrust on the plate
$\rho ={\rho }_{w}g{A}_x$
$=10^3\times 9.8\times 6\times 5=294\times 10^{3}N$