Eduprobe
Question:
A solid sphere of radius R and density ρ is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are):
the net elongation of the spring is 4πR³ρg/3k
the net elongation of the spring is 8πR³ρg/3k
the light sphere is partially submerged.
the light sphere is completely submerged.
the net elongation of the spring is 4πR³ρg/3k
the light sphere is completely submerged.
the net elongation of the spring is 8πR³ρg/3k
the light sphere is partially submerged.
Solution:
Sol (A,D)
At equilibrium,
(4/3)πR³(2ρ)g = (4/3)πR³ρg + T
T = (4/3)πR³ρg
Δl = (4/3)kπR³ρg
For equilibrium of the complete system, the net force of buoyancy must be equal to the total weight of the spheres, which holds in the given problem. So both the spheres are completely submerged.