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 50N.
• 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 50N.

C

the spring potential energy is 12.5 J.

At equilibrium

$kx=Mg=F_B$

$kx=mg(1-\frac{\sigma }{\rho })$

$\Rightarrow 100\left(x\right)=100(1-\frac{1000}{2000})$

$\Rightarrow x=0.5m$

$F_B=50N$

$P.E.=\frac{1}{2}k{x}^2=12.5J$