UPSEE Solved Model Paper 3

The cube is in equilibrium under three forces as, spring force kx, where x = elongation of the spring,

Gravitational force ω, weight of the cube = mg
Buoyant force,
Fb (or upward thrust) imparted by the liquid on the cube given as Fb = Vdg , where V = volume of the immersed portion of the cube.
For complete immersion, V = volume ofthe cube
For equilibrium of the cube
kx + Fb = mg
⇒ x =

mg−Fb

k

=

mg−Vdg

k

where, V = (

m

D

)
⇒ x =

mg

k

(1−

d

D

)