Question

An open pan P filled with water (density ${\rho }_w$ )
is placed on a vertical rod, maintaining equilibrium. A block of density $\rho$ is placed on one side of the pan as shown in the figure. Water depth is more than height of the block.

• A. Equilibrium will be maintained only if $\rho$ < ${\rho }_w$.
• B. Equilibrium will be maintained only if $\rho$ $\le$ ${\rho }_w$.
• C. Equilibrium will be maintained for all relations between $\rho$ and ${\rho }_w$.
• D. Equilibrium will not be maintained in all cases.

Answer 1

The correct option is B Equilibrium will be maintained only if $\rho$ $\le$ ${\rho }_w$.

R.E.F image

Suppose Density of block is $\rho$

Consider FBD of block

Ref. image

The buoyant face is equal to the

weight of the displaced fluid according to Archimedes

principle.

If the block is in equilibrium, then the weight of

the fluid displaced is balancing the block.

This weight of fluid displaced balancing the block is

visualized same as absence of block or the

face to same as that of displaced fluid being

actually there.

If the buoyant face is unable to balance the

weight of the block, the block will and at the

bottom of the reset a contact force gets exerted

which will disrupt the equilibrium of the total system.