Question

The minimum work required to be done by the person pushing the cube to the base of the tank is:

• A. $1250J$
• B. $2500J$
• C. $1875J$
• D. None of these

Answer 1

The correct option is A $1250J$

As the cube is half immersed in water initially i.e $h=0.5m$

Let the cube is further pushed into the tank by amount of $x$.

Weight of the cube $W=5000N$

Buoyancy force acting on the cube $B_x=1000(0.5+x)g$

$\therefore$ $F_x=B_x-W=1000(0.5+x)\left(10\right)-5000=10000x$

Thus the work done by the force $W_x={\int }_0^{0.5}{F}_{x}dx$

$\therefore$ $W_x={\int }_0^{0.5}10000xdx$

OR $W_x=10000\times \frac{x^2}{2}{|}_0^{0.5}=10000\times \frac{(0.5{)}^2}{2}=1250$ J