A right circular cylinder has a mass m,radius | vedclass

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(D) The forces acting on the cylinder are the gravitational force $(mg)$ acting downwards and the buoyant force $(F_b)$ acting upwards.According to Ar

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$|\pi r^2 \rho gh - mg|$

Vedclass · Answer

(D) The forces acting on the cylinder are the gravitational force $(mg)$ acting downwards and the buoyant force $(F_b)$ acting upwards.According to Archimedes' principle,the buoyant force is equal to the weight of the fluid displaced by the cylinder.The volume of the cylinder is $V = \pi r^2 h$.Therefore,the buoyant force is $F_b = \rho Vg = \rho (\pi r^2 h) g = \pi r^2 \rho gh$.The net force $F_{net}$ on the cylinder is the difference between the buoyant force and the gravitational force.$F_{net} = F_b - mg = \pi r^2 \rho gh - mg$.Since we are asked for the magnitude of the net force,we take the absolute value:$|F_{net}| = |\pi r^2 \rho gh - mg|$.

$A$ right circular cylinder has a mass $m$,radius $r$,and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$,as shown in the diagram,and is released. What is the magnitude of the net force on the cylinder initially?

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