Question

A block of density $2000kg/m^3$ and mass 10 kg is suspended by a spring stiffness 100 N/m. The other end of the spring is attached to a fixed support. The block is completely submerged in a liquid of density $1000kg/m^3$. If the block is in equilibrium position, then:

• A. The elongation of the spring is 1 cm
• B. The magnitude of buoyant force acting on the block is 50 N
• C. The spring potential energy is 12.5 J
• D. Magnitude of spring force on the block is greater than the weight of the block.

Answer 1

Answer: (B), (C)

The correct options are
B The magnitude of buoyant force acting on the block is 50 N
C The spring potential energy is 12.5 J

Initial elongation in spring
$kx=mg$
$x=\frac{10\times 10}{100}$
$x=1m$
When immersed in liquid
$F_B=\frac{m}{\rho }{\rho }_{L}g$
$=\frac{10}{2000}\times 1000\times 10$
$F_B=50N$
New elongation:
$kx=mg-F_B$
$x=0.5m$
P.E. $=\frac{1}{2}k{x}^2=12.5J$