Question

A ball of mass $m$ and density $\frac{\rho }{2}$ is completely immersed in a liquid of density $\rho$ contained in an accelerating vessel as shown. Select the correct answer.

• A. P-1; Q-3; R-2; S-4
• B. P-4; Q-1; R-2; S-3
• C. P-3; Q-4; R-2; S-1
• D. P-1; Q-4; R-3; S-2

Answer 1

The correct option is A P-1; Q-3; R-2; S-4



Buoyant force on ball = $\sqrt{2}\left(2mg\right)$
Force on ball w.r.t. vessel, where $F_p$ is peudo force on ball in frame of vessel.


Since, force on ball in frame of vessel is along upward normal to surface of liquid,ball will rise.
$\left(P\right)$ - 1, 3, 4

Buoyant force on ball $=v\rho (g+g)=4mg$

Force on ball w.r.t vessel


Since, force on ball in frame of vessel is along upward normal to surface of liquid, ball will rise.
$\left(Q\right)$ - 3, 4

Buoyant force on ball $=v\rho (g-g)=0$
Force on ball w.r.t. vessel is absent.
Since, force on ball in frame of vessel is zero, ball will remain stationary.
$\left(R\right)$ - 2


Since, acceleration of vessel is $g/2$ downwards. Therefore,
Buoyant force on ball$=v\rho \sqrt{(g/2{)}^2+(g{)}^2+2\left(g\right)\left(g/2\right)cos{120}^{\circ }}=\sqrt{3}mg$
Since, force on ball in frame of vessel is along upward normal to surface of liquid, ball will rise.
$\left(S\right)$ - 3, 4