Question

A rectangular plate $2 m \times 3 m$ is immersed in water in such a way that its greatest and least depth are $6\, m$ and $4 \,m$ 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 $=2\, m \times 5\, m$ and
Greatest and least depths of the plate are $6\, m$ and $4\, m$.
We know that area of the plate $A=2 \times 3=6 m ^{2}$
and depth of centre of the plate
$x=\frac{6+4}{2}=5\, m$
$\therefore $ Total thrust on the plate
$\rho =\rho_{w} g A _{x} $
$=10^{3} \times 9.8 \times 6 \times 5=294 \times 10^{3} \,N$